0=2x^2+5x-4

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Solution for 0=2x^2+5x-4 equation:


Simplifying
0 = 2x2 + 5x + -4

Reorder the terms:
0 = -4 + 5x + 2x2

Solving
0 = -4 + 5x + 2x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2x2 + -2x2 = 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}

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