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Simplifying -2x2 + -418x + 3600 = 0 Reorder the terms: 3600 + -418x + -2x2 = 0 Solving 3600 + -418x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1800 + -209x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1800 + -209x + -1x2)' equal to zero and attempt to solve: Simplifying 1800 + -209x + -1x2 = 0 Solving 1800 + -209x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1800 + 209x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 209x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 209x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 209x + x2 = 0 + 1800 209x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 209x + x2 = 1800 The x term is 209x. Take half its coefficient (104.5). Square it (10920.25) and add it to both sides. Add '10920.25' to each side of the equation. 209x + 10920.25 + x2 = 1800 + 10920.25 Reorder the terms: 10920.25 + 209x + x2 = 1800 + 10920.25 Combine like terms: 1800 + 10920.25 = 12720.25 10920.25 + 209x + x2 = 12720.25 Factor a perfect square on the left side: (x + 104.5)(x + 104.5) = 12720.25 Calculate the square root of the right side: 112.784085757 Break this problem into two subproblems by setting (x + 104.5) equal to 112.784085757 and -112.784085757.Subproblem 1
x + 104.5 = 112.784085757 Simplifying x + 104.5 = 112.784085757 Reorder the terms: 104.5 + x = 112.784085757 Solving 104.5 + x = 112.784085757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-104.5' to each side of the equation. 104.5 + -104.5 + x = 112.784085757 + -104.5 Combine like terms: 104.5 + -104.5 = 0.0 0.0 + x = 112.784085757 + -104.5 x = 112.784085757 + -104.5 Combine like terms: 112.784085757 + -104.5 = 8.284085757 x = 8.284085757 Simplifying x = 8.284085757Subproblem 2
x + 104.5 = -112.784085757 Simplifying x + 104.5 = -112.784085757 Reorder the terms: 104.5 + x = -112.784085757 Solving 104.5 + x = -112.784085757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-104.5' to each side of the equation. 104.5 + -104.5 + x = -112.784085757 + -104.5 Combine like terms: 104.5 + -104.5 = 0.0 0.0 + x = -112.784085757 + -104.5 x = -112.784085757 + -104.5 Combine like terms: -112.784085757 + -104.5 = -217.284085757 x = -217.284085757 Simplifying x = -217.284085757Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.284085757, -217.284085757}Solution
x = {8.284085757, -217.284085757}
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