0=-4x^2-10x+15

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Solution for 0=-4x^2-10x+15 equation:


Simplifying
0 = -4x2 + -10x + 15

Reorder the terms:
0 = 15 + -10x + -4x2

Solving
0 = 15 + -10x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 10x + 4x2 = 15 + -10x + -4x2 + -15 + 10x + 4x2

Reorder the terms:
-15 + 10x + 4x2 = 15 + -15 + -10x + 10x + -4x2 + 4x2

Combine like terms: 15 + -15 = 0
-15 + 10x + 4x2 = 0 + -10x + 10x + -4x2 + 4x2
-15 + 10x + 4x2 = -10x + 10x + -4x2 + 4x2

Combine like terms: -10x + 10x = 0
-15 + 10x + 4x2 = 0 + -4x2 + 4x2
-15 + 10x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15 + 10x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 2.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 2.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 2.5x + x2 = 0 + 3.75
2.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
2.5x + x2 = 3.75

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 = 3.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 3.75 + 1.5625

Combine like terms: 3.75 + 1.5625 = 5.3125
1.5625 + 2.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.304886114 and -2.304886114.

Subproblem 1

x + 1.25 = 2.304886114 Simplifying x + 1.25 = 2.304886114 Reorder the terms: 1.25 + x = 2.304886114 Solving 1.25 + x = 2.304886114 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 = 2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.304886114 + -1.25 x = 2.304886114 + -1.25 Combine like terms: 2.304886114 + -1.25 = 1.054886114 x = 1.054886114 Simplifying x = 1.054886114

Subproblem 2

x + 1.25 = -2.304886114 Simplifying x + 1.25 = -2.304886114 Reorder the terms: 1.25 + x = -2.304886114 Solving 1.25 + x = -2.304886114 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 = -2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.304886114 + -1.25 x = -2.304886114 + -1.25 Combine like terms: -2.304886114 + -1.25 = -3.554886114 x = -3.554886114 Simplifying x = -3.554886114

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.054886114, -3.554886114}

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