Question

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3

Answer 1

Answer: The following are the steps that Patel could use to solve the quadratic equation:

Rewrite the equation in standard form: 8x^2 + 16x + 3 = 0

Divide both sides of the equation by 8 to simplify: x^2 + 2x + 3/8 = 0

Complete the square by adding and subtracting (2/2)^2 = 1 from the left-hand side of the equation:

x^2 + 2x + 1 - 1 + 3/8 = 0

Simplify the left-hand side of the equation: (x + 1)^2 = 1/8

Take the square root of both sides of the equation:

x + 1 = ±√(1/8)

Solve for x:

x = -1 ± √(1/8)

Therefore, the three options that Patel could use to solve the quadratic equation are:

Complete the square by adding and subtracting (2/2)^2 = 1 from the left-hand side of the equation.

Simplify the left-hand side of the equation: (x + 1)^2 = 1/8.

Take the square root of both sides of the equation: x + 1 = ±√(1/8).

Explanation: