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Simplifying 220 = 2(x + 5)(x + -2) Reorder the terms: 220 = 2(5 + x)(x + -2) Reorder the terms: 220 = 2(5 + x)(-2 + x) Multiply (5 + x) * (-2 + x) 220 = 2(5(-2 + x) + x(-2 + x)) 220 = 2((-2 * 5 + x * 5) + x(-2 + x)) 220 = 2((-10 + 5x) + x(-2 + x)) 220 = 2(-10 + 5x + (-2 * x + x * x)) 220 = 2(-10 + 5x + (-2x + x2)) Combine like terms: 5x + -2x = 3x 220 = 2(-10 + 3x + x2) 220 = (-10 * 2 + 3x * 2 + x2 * 2) 220 = (-20 + 6x + 2x2) Solving 220 = -20 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 220 + 20 = 240 240 + -6x + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2 Reorder the terms: 240 + -6x + -2x2 = -20 + 20 + 6x + -6x + 2x2 + -2x2 Combine like terms: -20 + 20 = 0 240 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 240 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 240 + -6x + -2x2 = 0 + 2x2 + -2x2 240 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 240 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(120 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(120 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 120 + -3x + -1x2 = 0 Solving 120 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + 3x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 3x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 3x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 3x + x2 = 0 + 120 3x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 3x + x2 = 120 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 120 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 120 + 2.25 Combine like terms: 120 + 2.25 = 122.25 2.25 + 3x + x2 = 122.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + 1.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + 1.5 = 11.056672194 Simplifying x + 1.5 = 11.056672194 Reorder the terms: 1.5 + x = 11.056672194 Solving 1.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.056672194 + -1.5 x = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 x = 9.556672194 Simplifying x = 9.556672194Subproblem 2
x + 1.5 = -11.056672194 Simplifying x + 1.5 = -11.056672194 Reorder the terms: 1.5 + x = -11.056672194 Solving 1.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.056672194 + -1.5 x = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 x = -12.556672194 Simplifying x = -12.556672194Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.556672194, -12.556672194}Solution
x = {9.556672194, -12.556672194}
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