2x^2-40x-144=0

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Solution for 2x^2-40x-144=0 equation:


Simplifying
2x2 + -40x + -144 = 0

Reorder the terms:
-144 + -40x + 2x2 = 0

Solving
-144 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-72 + -20x + x2)' equal to zero and attempt to solve: Simplifying -72 + -20x + x2 = 0 Solving -72 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -20x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -20x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -20x + x2 = 0 + 72 -20x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -20x + x2 = 72 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 = 72 + 100 Reorder the terms: 100 + -20x + x2 = 72 + 100 Combine like terms: 72 + 100 = 172 100 + -20x + x2 = 172 Factor a perfect square on the left side: (x + -10)(x + -10) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + -10) equal to 13.114877049 and -13.114877049.

Subproblem 1

x + -10 = 13.114877049 Simplifying x + -10 = 13.114877049 Reorder the terms: -10 + x = 13.114877049 Solving -10 + x = 13.114877049 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 = 13.114877049 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.114877049 + 10 x = 13.114877049 + 10 Combine like terms: 13.114877049 + 10 = 23.114877049 x = 23.114877049 Simplifying x = 23.114877049

Subproblem 2

x + -10 = -13.114877049 Simplifying x + -10 = -13.114877049 Reorder the terms: -10 + x = -13.114877049 Solving -10 + x = -13.114877049 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 = -13.114877049 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.114877049 + 10 x = -13.114877049 + 10 Combine like terms: -13.114877049 + 10 = -3.114877049 x = -3.114877049 Simplifying x = -3.114877049

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.114877049, -3.114877049}

Solution

x = {23.114877049, -3.114877049}

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