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Simplifying 2x2 + -18x + -680 = 0 Reorder the terms: -680 + -18x + 2x2 = 0 Solving -680 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-340 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-340 + -9x + x2)' equal to zero and attempt to solve: Simplifying -340 + -9x + x2 = 0 Solving -340 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + -9x + 340 + x2 = 0 + 340 Reorder the terms: -340 + 340 + -9x + x2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + -9x + x2 = 0 + 340 -9x + x2 = 0 + 340 Combine like terms: 0 + 340 = 340 -9x + x2 = 340 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 340 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 340 + 20.25 Combine like terms: 340 + 20.25 = 360.25 20.25 + -9x + x2 = 360.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 360.25 Calculate the square root of the right side: 18.980252896 Break this problem into two subproblems by setting (x + -4.5) equal to 18.980252896 and -18.980252896.Subproblem 1
x + -4.5 = 18.980252896 Simplifying x + -4.5 = 18.980252896 Reorder the terms: -4.5 + x = 18.980252896 Solving -4.5 + x = 18.980252896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 18.980252896 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 18.980252896 + 4.5 x = 18.980252896 + 4.5 Combine like terms: 18.980252896 + 4.5 = 23.480252896 x = 23.480252896 Simplifying x = 23.480252896Subproblem 2
x + -4.5 = -18.980252896 Simplifying x + -4.5 = -18.980252896 Reorder the terms: -4.5 + x = -18.980252896 Solving -4.5 + x = -18.980252896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -18.980252896 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -18.980252896 + 4.5 x = -18.980252896 + 4.5 Combine like terms: -18.980252896 + 4.5 = -14.480252896 x = -14.480252896 Simplifying x = -14.480252896Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.480252896, -14.480252896}Solution
x = {23.480252896, -14.480252896}
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