Question

Solve 2x^2 = 5x + 4 using the quadratic formula. Round your answer to the nearest tenth. (Points : 1)
{3.1, -0.6}
{-3.1, 0.6}
{1.9, -0.6}
{-1.9, 0.6}

Answer 1

Simplifying
2x2 = 5x + 4

Reorder the terms:
2x2 = 4 + 5x

Solving
2x2 = 4 + 5x

Solving for variable 'x'.

Reorder the terms:
-4 + -5x + 2x2 = 4 + 5x + -4 + -5x

Reorder the terms:
-4 + -5x + 2x2 = 4 + -4 + 5x + -5x

Combine like terms: 4 + -4 = 0
-4 + -5x + 2x2 = 0 + 5x + -5x
-4 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-4 + -5x + 2x2 = 0

Begin completing the square. Divide all terms by
2 the coefficient of the squared term:

Divide each side by '2'.
-2 + -2.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.5x + x2 = 0 + 2
-2.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.5x + x2 = 2

The x term is -2.5x. Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 2 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 2 + 1.5625

Combine like terms: 2 + 1.5625 = 3.5625
1.5625 + -2.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting
(x + -1.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
x + -1.25 = 1.887458609

Simplifying
x + -1.25 = 1.887458609

Reorder the terms:
-1.25 + x = 1.887458609

Solving
-1.25 + x = 1.887458609

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.887458609 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.887458609 + 1.25
x = 1.887458609 + 1.25

Combine like terms: 1.887458609 + 1.25 = 3.137458609
x = 3.137458609

Simplifying
x = 3.137458609

Subproblem 2
x + -1.25 = -1.887458609

Simplifying
x + -1.25 = -1.887458609

Reorder the terms:
-1.25 + x = -1.887458609

Solving
-1.25 + x = -1.887458609

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.887458609 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.887458609 + 1.25
x = -1.887458609 + 1.25

Combine like terms: -1.887458609 + 1.25 = -0.637458609
x = -0.637458609

Simplifying
x = -0.637458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.137458609, -0.637458609}

Answer 2

Id say A.