how to solve a quadratic equation by completing a square?
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Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
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Substitute the first pair of values into the general form of the quadratic equation: f(x) = ax^2 + bx + c. Solve for a. For example, 5 = a(1^2) + b(1) + c simplifies to a = -b - c + 5. Substitute the second ordered pair and the value of a into the general equation.
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Factoring the Polynomial Write the equation (x2-2) as the difference of two squares employing the terms' square roots. The expression (x2-2) becomes (x-√2) (x+√2).
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['Step 1: Getting Started. You should know that a quadratic equation looks something like this: x^2-3x+2=0 or ax^2+bx+c=0. ... ', 'Step 2: The Equation. Look at the first picture and put that on your calculator. ... ', 'Step 3: Displaying Results. Press program, then the right arrow, then 3. ... ', 'Step 4: Using the Program.']
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The quadratic formula. The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) .
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Solve equations of the form ax2+c=0 by extracting the roots. Extracting roots involves isolating the square and then applying the square root property. Remember to include “±” when taking the square root of both sides. After applying the square root property, solve each of the resulting equations.
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We complete the square by taking half of the coefficient of our x term, squaring it, and adding it to both sides of the equation. Since the coefficient of our x term is 10, half of it would be 5, and squaring it gives us 25start color #11accd, 25, end color #11accd.
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['Solution.', 'Step 1: Add or subtract the constant term to obtain an equation of the form x2+bx=c. ... ', 'Step 2: Use (b2)2 to determint the value that completes the square. ... ', 'Step 3: Add (b2)2 to both sides of the equation and complete the square.', 'Step 4: Solve by extracting roots.', 'Answer:']
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Step 1: To use the quadratic formula, the equation must be equal to zero, so move the –4x back to the left hand side. Step 2: Identify a, b, and c and plug them into the quadratic formula. In this case a = 3, b = 4, and c = 8. Step 3: Use the order of operations to simplify the quadratic formula.
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['You can “manually” solve the equation on the calculator, meaning that if you want to solve the equation ax^2 + bx + c, you basically plug in the quadratic formula into the calculator and hit enter. ... ', 'The second way is faster, but be sure to check that your teacher is okay with you using it.']
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To solve an equation by using the square root property, you will first isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable. Make sure to write the final answer in simplified form.
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To solve, first add 4 to both sides of the equation. X^2–4+4=0+4. You then have x^2=4. Next, take the square root of both sides, which leaves x=2.
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A perfect square trinomial can be factored, so the equation can then be solved by taking the square root of both sides. Solve the equation x2 + 8x + 5 = 0 by completing the square. First, rewrite the equation in the form x2 + bx = c. Add the appropriate constant to complete the square, then simplify.
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['Isolate the radical on one side of the equation.', 'Square both sides of the equation.', 'Solve the new equation.', 'Check the answer.']
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The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) .
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Factoring involves setting each factor equal to zero and solving each factor. When the quadratic has a squared part and a number part (for example, ), take the square root. When the equation cannot be solved by factoring and is not in the form ready for a square root, complete the square or use the quadratic formula.
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['Problem 1. Solve for x: x2-15x+56 = 0. A. x = 14 or x = 4. B. x = 8 or x = 7. C. x = 28 or x = 2. ... ', 'Problem 2. Find x if 2x2+7x+4 = 0. A. - 7 ± √17 / 4. B. - 7 ± √7 / 4. C. ... ', 'Problem 3. For what value of k does the equation x2-12x+k = 0 have real and equal roots? A. B. C. D. Answer 3.']