how to solve quadratic equation by extracting the roots?
116746
['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. ... ', 'After applying the square root property, solve each of the resulting equations. ... ', 'Solve any quadratic equation by completing the square.']
328339
['Make both equations into "y =" format.', 'Set them equal to each other.', 'Simplify into "= 0" format (like a standard Quadratic Equation)', 'Solve the Quadratic Equation!', 'Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.']
712136
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. The product of the roots of a quadratic equation is equal to the constant term (the third term), divided by the leading coefficient.
219004
The square root method can be used for solving quadratic equations in the form "x² = b." This method can yield two answers, as the square root of a number can be a negative or a positive number. If an equation can be expressed in this form, it can be solved by finding the square roots of x.
1360714
The first step is to write the equation as quadratic = linear. Then you just take all values to one side so that you remain with 0 on the other. Next solve the quadratic equation so that you end up with the possible values of x.
1039598
Roots are also called x-intercepts or zeros. ... By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.
329427
For a quadratic equation ax2+bx+c = 0 (where a, b and c are coefficients), it's roots is given by following the formula. The term b2-4ac is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.
1315032
['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:']
94084
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.
181514
['Isolate the radical on one side of the equation.', 'Square both sides of the equation.', 'Solve the new equation.', 'Check the answer.']
160015
Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring.
581744
For a quadratic equation ax2+bx+c = 0 (where a, b and c are coefficients), it's roots is given by following the formula. The term b2-4ac is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots. If discriminant is greater than 0, the roots are real and different.
103194
An alternative method to solve a quadratic equation is to complete the square. To solve an equation of the form x 2 + b x + c = 0 consider the expression ( x + b 2 ) 2 + c . ( x + b 2 ) 2 + c expands to x 2 + b x + ( b 2 ) 2 + c , which is the same as the left-hand side of the original equation but with an extra term.
292312
The general approach is to collect all x2 terms on one side of the equation while keeping the constants to the opposite side. After doing so, the next obvious step is to take the square roots of both sides to solve for the value of x. Always attach the ± symbol when you get the square root of the constant.
1348760
['#include<stdio.h>', '#include<math.h>', 'int main(){', 'float a,b,c;', 'float d,root1,root2;', 'printf("Enter a, b and c of quadratic equation: ");', 'scanf("%f%f%f",&a,&b,&c);', 'd = b * b - 4 * a * c;']
54352
In other words, the quadratic formula is simply just ax^2+bx+c = 0 in terms of x. So the roots of ax^2+bx+c = 0 would just be the quadratic equation, which is: (-b+-√b^2-4ac) / 2a.
238481
['#include<stdio.h>', '#include<math.h>', 'int main(){', 'float a,b,c;', 'float d,root1,root2;', 'printf("Enter quadratic equation in the format ax^2+bx+c: ");', 'scanf("%fx^2%fx%f",&a,&b,&c);', 'd = b * b - 4 * a * c;']