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Simplifying (15 + -1x)(9 + -1x)(3) = 364.5 Reorder the terms for easier multiplication: 3(15 + -1x)(9 + -1x) = 364.5 Multiply (15 + -1x) * (9 + -1x) 3(15(9 + -1x) + -1x * (9 + -1x)) = 364.5 3((9 * 15 + -1x * 15) + -1x * (9 + -1x)) = 364.5 3((135 + -15x) + -1x * (9 + -1x)) = 364.5 3(135 + -15x + (9 * -1x + -1x * -1x)) = 364.5 3(135 + -15x + (-9x + 1x2)) = 364.5 Combine like terms: -15x + -9x = -24x 3(135 + -24x + 1x2) = 364.5 (135 * 3 + -24x * 3 + 1x2 * 3) = 364.5 (405 + -72x + 3x2) = 364.5 Solving 405 + -72x + 3x2 = 364.5 Solving for variable 'x'. Reorder the terms: 405 + -364.5 + -72x + 3x2 = 364.5 + -364.5 Combine like terms: 405 + -364.5 = 40.5 40.5 + -72x + 3x2 = 364.5 + -364.5 Combine like terms: 364.5 + -364.5 = 0.0 40.5 + -72x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.5 + -24x + x2 = 0.0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -24x + -13.5 + x2 = 0.0 + -13.5 Reorder the terms: 13.5 + -13.5 + -24x + x2 = 0.0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -24x + x2 = 0.0 + -13.5 -24x + x2 = 0.0 + -13.5 Combine like terms: 0.0 + -13.5 = -13.5 -24x + x2 = -13.5 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -13.5 + 144 Reorder the terms: 144 + -24x + x2 = -13.5 + 144 Combine like terms: -13.5 + 144 = 130.5 144 + -24x + x2 = 130.5 Factor a perfect square on the left side: (x + -12)(x + -12) = 130.5 Calculate the square root of the right side: 11.423659659 Break this problem into two subproblems by setting (x + -12) equal to 11.423659659 and -11.423659659.Subproblem 1
x + -12 = 11.423659659 Simplifying x + -12 = 11.423659659 Reorder the terms: -12 + x = 11.423659659 Solving -12 + x = 11.423659659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.423659659 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.423659659 + 12 x = 11.423659659 + 12 Combine like terms: 11.423659659 + 12 = 23.423659659 x = 23.423659659 Simplifying x = 23.423659659Subproblem 2
x + -12 = -11.423659659 Simplifying x + -12 = -11.423659659 Reorder the terms: -12 + x = -11.423659659 Solving -12 + x = -11.423659659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.423659659 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.423659659 + 12 x = -11.423659659 + 12 Combine like terms: -11.423659659 + 12 = 0.576340341 x = 0.576340341 Simplifying x = 0.576340341Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.423659659, 0.576340341}
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