Question

What are the approximate solutions of 2x^2 + 5x = 4 rounded to the nearest hundredth?

Answer 1

Simplifying
2x2 + 5x = 4

Reorder the terms:
5x + 2x2 = 4

Solving
5x + 2x2 = 4

Solving for variable 'x'.

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

Combine like terms: 4 + -4 = 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 = 0.637458609
x = 0.637458609

Simplifying
x = 0.637458609

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 = -3.137458609
x = -3.137458609

Simplifying
x = -3.137458609

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

Answer 2

Let me know if You want me to round them :P

Answer 3

No real solutions
x ≈ −6.27 and x ≈ 1.27
x ≈ −0.64 and x ≈ 3.14
x ≈ −3.14 and x ≈ 0.64

Answer 4

yea i need them rounded

Answer 5

Its C.

Answer 6

thnx

Answer 7

why not just use the general quadratic formula

\[x = \frac{-5 \pm \sqrt{5^2 - 4 \times2\times -4}}{2 \times 2}\]

just seems simpler to me...