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Simplifying 2x(x + -30) = 90 Reorder the terms: 2x(-30 + x) = 90 (-30 * 2x + x * 2x) = 90 (-60x + 2x2) = 90 Solving -60x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -60x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -60x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -30x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -30x + x2)' equal to zero and attempt to solve: Simplifying -45 + -30x + x2 = 0 Solving -45 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -30x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -30x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -30x + x2 = 0 + 45 -30x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -30x + x2 = 45 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 45 + 225 Reorder the terms: 225 + -30x + x2 = 45 + 225 Combine like terms: 45 + 225 = 270 225 + -30x + x2 = 270 Factor a perfect square on the left side: (x + -15)(x + -15) = 270 Calculate the square root of the right side: 16.431676725 Break this problem into two subproblems by setting (x + -15) equal to 16.431676725 and -16.431676725.Subproblem 1
x + -15 = 16.431676725 Simplifying x + -15 = 16.431676725 Reorder the terms: -15 + x = 16.431676725 Solving -15 + x = 16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 16.431676725 + 15 Combine like terms: -15 + 15 = 0 0 + x = 16.431676725 + 15 x = 16.431676725 + 15 Combine like terms: 16.431676725 + 15 = 31.431676725 x = 31.431676725 Simplifying x = 31.431676725Subproblem 2
x + -15 = -16.431676725 Simplifying x + -15 = -16.431676725 Reorder the terms: -15 + x = -16.431676725 Solving -15 + x = -16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -16.431676725 + 15 Combine like terms: -15 + 15 = 0 0 + x = -16.431676725 + 15 x = -16.431676725 + 15 Combine like terms: -16.431676725 + 15 = -1.431676725 x = -1.431676725 Simplifying x = -1.431676725Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.431676725, -1.431676725}Solution
x = {31.431676725, -1.431676725}
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