-0.146x^2+0.96x+7.5=0

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Solution for -0.146x^2+0.96x+7.5=0 equation:


Simplifying
-0.146x2 + 0.96x + 7.5 = 0

Reorder the terms:
7.5 + 0.96x + -0.146x2 = 0

Solving
7.5 + 0.96x + -0.146x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.146 the coefficient of the squared term: 

Divide each side by '-0.146'.
-51.36986301 + -6.575342466x + x2 = 0

Move the constant term to the right:

Add '51.36986301' to each side of the equation.
-51.36986301 + -6.575342466x + 51.36986301 + x2 = 0 + 51.36986301

Reorder the terms:
-51.36986301 + 51.36986301 + -6.575342466x + x2 = 0 + 51.36986301

Combine like terms: -51.36986301 + 51.36986301 = 0.00000000
0.00000000 + -6.575342466x + x2 = 0 + 51.36986301
-6.575342466x + x2 = 0 + 51.36986301

Combine like terms: 0 + 51.36986301 = 51.36986301
-6.575342466x + x2 = 51.36986301

The x term is -6.575342466x.  Take half its coefficient (-3.287671233).
Square it (10.80878214) and add it to both sides.

Add '10.80878214' to each side of the equation.
-6.575342466x + 10.80878214 + x2 = 51.36986301 + 10.80878214

Reorder the terms:
10.80878214 + -6.575342466x + x2 = 51.36986301 + 10.80878214

Combine like terms: 51.36986301 + 10.80878214 = 62.17864515
10.80878214 + -6.575342466x + x2 = 62.17864515

Factor a perfect square on the left side:
(x + -3.287671233)(x + -3.287671233) = 62.17864515

Calculate the square root of the right side: 7.885343693

Break this problem into two subproblems by setting 
(x + -3.287671233) equal to 7.885343693 and -7.885343693.

Subproblem 1

x + -3.287671233 = 7.885343693 Simplifying x + -3.287671233 = 7.885343693 Reorder the terms: -3.287671233 + x = 7.885343693 Solving -3.287671233 + x = 7.885343693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.287671233' to each side of the equation. -3.287671233 + 3.287671233 + x = 7.885343693 + 3.287671233 Combine like terms: -3.287671233 + 3.287671233 = 0.000000000 0.000000000 + x = 7.885343693 + 3.287671233 x = 7.885343693 + 3.287671233 Combine like terms: 7.885343693 + 3.287671233 = 11.173014926 x = 11.173014926 Simplifying x = 11.173014926

Subproblem 2

x + -3.287671233 = -7.885343693 Simplifying x + -3.287671233 = -7.885343693 Reorder the terms: -3.287671233 + x = -7.885343693 Solving -3.287671233 + x = -7.885343693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.287671233' to each side of the equation. -3.287671233 + 3.287671233 + x = -7.885343693 + 3.287671233 Combine like terms: -3.287671233 + 3.287671233 = 0.000000000 0.000000000 + x = -7.885343693 + 3.287671233 x = -7.885343693 + 3.287671233 Combine like terms: -7.885343693 + 3.287671233 = -4.59767246 x = -4.59767246 Simplifying x = -4.59767246

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.173014926, -4.59767246}

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