Solve the quadratic equation by completing the square.
4x2 + 2x - 7 = 0
A) x = 1 ± square root of 29/4
B) x = −1 ± square root of 29/4
C) x = −1 ± square root of 29/8
D) x = −1 ± square root of 29/16
Please help me!
To solve the quadratic equation 4x^2 + 2x - 7 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
4x^2 + 2x = 7
Step 2: Divide the entire equation by the coefficient of x^2 to make it leading coefficient 1:
x^2 + (2/4)x = 7/4
Simplifying it further:
x^2 + (1/2)x = 7/4
Step 3: To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 + (1/2)x + (1/4)^2 = 7/4 + (1/4)^2
Simplifying it further:
x^2 + (1/2)x + (1/16) = 7/4 + 1/16
x^2 + (1/2)x + (1/16) = 28/16 + 1/16
x^2 + (1/2)x + (1/16) = 29/16
Step 4: Rewrite the left side of the equation as a perfect square trinomial and simplify the right side:
(x + 1/4)^2 = 29/16
Step 5: Take the square root of both sides of the equation and solve for x:
x + 1/4 = ± square root of (29/16)
Step 6: Solve for x:
x = -1/4 ± square root of (29/16)
Step 7: Simplify the result:
x = -1/4 ± square root of 29 / square root of 16
Since the square root of 16 is 4, we can simplify further:
x = -1/4 ± square root of 29 / 4
Hence, the correct answer is:
x = -1 ± square root of 29/4
Therefore, the correct choice is A) x = -1 ± square root of 29/4.
4x2 + 2x - 7 = 0
4 x^2 + 2 x = 7
x^2 + (1/2)x = 7/4
x^2 + (1/2) x +(1/4)^2 = 7/4 + 1/16 = (28+1)/16
(x+1/4)^2 = 29/16
x+1/4 = +/- sqrt(29/16) = +/- (1/4)sqrt(29)
x = [ -1 +/- sqrt(29) ] / 4
be more careful with parentheses