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Simplifying 2x2 + -12x + -160 = 0 Reorder the terms: -160 + -12x + 2x2 = 0 Solving -160 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -6x + x2)' equal to zero and attempt to solve: Simplifying -80 + -6x + x2 = 0 Solving -80 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -6x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -6x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -6x + x2 = 0 + 80 -6x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -6x + x2 = 80 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 80 + 9 Reorder the terms: 9 + -6x + x2 = 80 + 9 Combine like terms: 80 + 9 = 89 9 + -6x + x2 = 89 Factor a perfect square on the left side: (x + -3)(x + -3) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -3) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -3 = 9.433981132 Simplifying x + -3 = 9.433981132 Reorder the terms: -3 + x = 9.433981132 Solving -3 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.433981132 + 3 x = 9.433981132 + 3 Combine like terms: 9.433981132 + 3 = 12.433981132 x = 12.433981132 Simplifying x = 12.433981132Subproblem 2
x + -3 = -9.433981132 Simplifying x + -3 = -9.433981132 Reorder the terms: -3 + x = -9.433981132 Solving -3 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.433981132 + 3 x = -9.433981132 + 3 Combine like terms: -9.433981132 + 3 = -6.433981132 x = -6.433981132 Simplifying x = -6.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.433981132, -6.433981132}Solution
x = {12.433981132, -6.433981132}
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