10x^2+9x-160=0

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Solution for 10x^2+9x-160=0 equation:


Simplifying
10x2 + 9x + -160 = 0

Reorder the terms:
-160 + 9x + 10x2 = 0

Solving
-160 + 9x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-16 + 0.9x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.9x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.9x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.9x + x2 = 0 + 16
0.9x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.9x + x2 = 16

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 16 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 16 + 0.2025

Combine like terms: 16 + 0.2025 = 16.2025
0.2025 + 0.9x + x2 = 16.2025

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 16.2025

Calculate the square root of the right side: 4.025232913

Break this problem into two subproblems by setting 
(x + 0.45) equal to 4.025232913 and -4.025232913.

Subproblem 1

x + 0.45 = 4.025232913 Simplifying x + 0.45 = 4.025232913 Reorder the terms: 0.45 + x = 4.025232913 Solving 0.45 + x = 4.025232913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 4.025232913 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 4.025232913 + -0.45 x = 4.025232913 + -0.45 Combine like terms: 4.025232913 + -0.45 = 3.575232913 x = 3.575232913 Simplifying x = 3.575232913

Subproblem 2

x + 0.45 = -4.025232913 Simplifying x + 0.45 = -4.025232913 Reorder the terms: 0.45 + x = -4.025232913 Solving 0.45 + x = -4.025232913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -4.025232913 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -4.025232913 + -0.45 x = -4.025232913 + -0.45 Combine like terms: -4.025232913 + -0.45 = -4.475232913 x = -4.475232913 Simplifying x = -4.475232913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.575232913, -4.475232913}

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