Solve the Following quadratic equations by completing the square.
7x(squared)+4x-13=8
7x^2 + 4x - 13 = 8
multiply by 7 to get a perfect square on the 2nd-degree term:
49x^2 + 28x = 147
49x^2 + 28x + 4 = 147 + 4
(7x+2)^2 = 151
7x = -2 ± √151
x = (-2 ± √151)/7
To solve the quadratic equation 7x^2 + 4x - 13 = 8 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
First, subtract 8 from both sides of the equation:
7x^2 + 4x - 13 - 8 = 0
7x^2 +4x - 21 = 0
Step 2: Divide the entire equation by the coefficient of x^2 (in this case, 7) to obtain a coefficient of 1 for x^2.
(7x^2 + 4x - 21) / 7 = 0
x^2 + (4/7)x - (3/7) = 0
Step 3: Focus on the terms involving x. Take half of the coefficient of x, square it, and add it to both sides of the equation.
In this case:
(4/7)/2 = 2/7
(2/7)^2 = 4/49
x^2 + (4/7)x + 4/49 - 3/7 = 4/49
x^2 + (4/7)x + 4/49 - 21/49 = 4/49
x^2 + (4/7)x - 17/49 = 0
Step 4: Rewrite the left side of the equation as a squared binomial.
In this case, the squared binomial is (x + (2/7))^2:
(x + (2/7))^2 = 17/49
Step 5: Take the square root of both sides of the equation, considering both the positive and negative square root.
x + (2/7) = ±√(17/49)
Step 6: Solve for x by isolating x on one side of the equation.
x = -2/7 ± √(17/49)
Thus, the solution to the quadratic equation 7x^2 + 4x - 13 = 8, after completing the square, is:
x = -2/7 ± √(17/49)