9x^2-180x-72=

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Solution for 9x^2-180x-72= equation:


Simplifying
9x2 + -180x + -72 = 0

Reorder the terms:
-72 + -180x + 9x2 = 0

Solving
-72 + -180x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + -20x + x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(-8 + -20x + x2)' equal to zero and attempt to solve: Simplifying -8 + -20x + x2 = 0 Solving -8 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -20x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -20x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -20x + x2 = 0 + 8 -20x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -20x + x2 = 8 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 8 + 100 Reorder the terms: 100 + -20x + x2 = 8 + 100 Combine like terms: 8 + 100 = 108 100 + -20x + x2 = 108 Factor a perfect square on the left side: (x + -10)(x + -10) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -10) equal to 10.392304845 and -10.392304845.

Subproblem 1

x + -10 = 10.392304845 Simplifying x + -10 = 10.392304845 Reorder the terms: -10 + x = 10.392304845 Solving -10 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.392304845 + 10 x = 10.392304845 + 10 Combine like terms: 10.392304845 + 10 = 20.392304845 x = 20.392304845 Simplifying x = 20.392304845

Subproblem 2

x + -10 = -10.392304845 Simplifying x + -10 = -10.392304845 Reorder the terms: -10 + x = -10.392304845 Solving -10 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.392304845 + 10 x = -10.392304845 + 10 Combine like terms: -10.392304845 + 10 = -0.392304845 x = -0.392304845 Simplifying x = -0.392304845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.392304845, -0.392304845}

Solution

x = {20.392304845, -0.392304845}

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