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Simplifying 0 = -20x2 + 380x + 3600 Reorder the terms: 0 = 3600 + 380x + -20x2 Solving 0 = 3600 + 380x + -20x2 Solving for variable 'x'. Combine like terms: 0 + -3600 = -3600 -3600 + -380x + 20x2 = 3600 + 380x + -20x2 + -3600 + -380x + 20x2 Reorder the terms: -3600 + -380x + 20x2 = 3600 + -3600 + 380x + -380x + -20x2 + 20x2 Combine like terms: 3600 + -3600 = 0 -3600 + -380x + 20x2 = 0 + 380x + -380x + -20x2 + 20x2 -3600 + -380x + 20x2 = 380x + -380x + -20x2 + 20x2 Combine like terms: 380x + -380x = 0 -3600 + -380x + 20x2 = 0 + -20x2 + 20x2 -3600 + -380x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -3600 + -380x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-180 + -19x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-180 + -19x + x2)' equal to zero and attempt to solve: Simplifying -180 + -19x + x2 = 0 Solving -180 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -19x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -19x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -19x + x2 = 0 + 180 -19x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -19x + x2 = 180 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 180 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 180 + 90.25 Combine like terms: 180 + 90.25 = 270.25 90.25 + -19x + x2 = 270.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 270.25 Calculate the square root of the right side: 16.439282223 Break this problem into two subproblems by setting (x + -9.5) equal to 16.439282223 and -16.439282223.Subproblem 1
x + -9.5 = 16.439282223 Simplifying x + -9.5 = 16.439282223 Reorder the terms: -9.5 + x = 16.439282223 Solving -9.5 + x = 16.439282223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 16.439282223 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 16.439282223 + 9.5 x = 16.439282223 + 9.5 Combine like terms: 16.439282223 + 9.5 = 25.939282223 x = 25.939282223 Simplifying x = 25.939282223Subproblem 2
x + -9.5 = -16.439282223 Simplifying x + -9.5 = -16.439282223 Reorder the terms: -9.5 + x = -16.439282223 Solving -9.5 + x = -16.439282223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -16.439282223 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -16.439282223 + 9.5 x = -16.439282223 + 9.5 Combine like terms: -16.439282223 + 9.5 = -6.939282223 x = -6.939282223 Simplifying x = -6.939282223Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.939282223, -6.939282223}Solution
x = {25.939282223, -6.939282223}
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