0=-0.16x^2+5x+8

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Solution for 0=-0.16x^2+5x+8 equation:


Simplifying
0 = -0.16x2 + 5x + 8

Reorder the terms:
0 = 8 + 5x + -0.16x2

Solving
0 = 8 + 5x + -0.16x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -5x + 0.16x2 = 8 + 5x + -0.16x2 + -8 + -5x + 0.16x2

Reorder the terms:
-8 + -5x + 0.16x2 = 8 + -8 + 5x + -5x + -0.16x2 + 0.16x2

Combine like terms: 8 + -8 = 0
-8 + -5x + 0.16x2 = 0 + 5x + -5x + -0.16x2 + 0.16x2
-8 + -5x + 0.16x2 = 5x + -5x + -0.16x2 + 0.16x2

Combine like terms: 5x + -5x = 0
-8 + -5x + 0.16x2 = 0 + -0.16x2 + 0.16x2
-8 + -5x + 0.16x2 = -0.16x2 + 0.16x2

Combine like terms: -0.16x2 + 0.16x2 = 0.00
-8 + -5x + 0.16x2 = 0.00

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

Divide each side by '0.16'.
-50 + -31.25x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -31.25x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -31.25x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -31.25x + x2 = 0 + 50
-31.25x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-31.25x + x2 = 50

The x term is -31.25x.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25x + 244.140625 + x2 = 50 + 244.140625

Reorder the terms:
244.140625 + -31.25x + x2 = 50 + 244.140625

Combine like terms: 50 + 244.140625 = 294.140625
244.140625 + -31.25x + x2 = 294.140625

Factor a perfect square on the left side:
(x + -15.625)(x + -15.625) = 294.140625

Calculate the square root of the right side: 17.150528418

Break this problem into two subproblems by setting 
(x + -15.625) equal to 17.150528418 and -17.150528418.

Subproblem 1

x + -15.625 = 17.150528418 Simplifying x + -15.625 = 17.150528418 Reorder the terms: -15.625 + x = 17.150528418 Solving -15.625 + x = 17.150528418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = 17.150528418 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = 17.150528418 + 15.625 x = 17.150528418 + 15.625 Combine like terms: 17.150528418 + 15.625 = 32.775528418 x = 32.775528418 Simplifying x = 32.775528418

Subproblem 2

x + -15.625 = -17.150528418 Simplifying x + -15.625 = -17.150528418 Reorder the terms: -15.625 + x = -17.150528418 Solving -15.625 + x = -17.150528418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = -17.150528418 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = -17.150528418 + 15.625 x = -17.150528418 + 15.625 Combine like terms: -17.150528418 + 15.625 = -1.525528418 x = -1.525528418 Simplifying x = -1.525528418

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.775528418, -1.525528418}

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