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Simplifying 150 = (20 + -1x)(12 + -1x) Multiply (20 + -1x) * (12 + -1x) 150 = (20(12 + -1x) + -1x * (12 + -1x)) 150 = ((12 * 20 + -1x * 20) + -1x * (12 + -1x)) 150 = ((240 + -20x) + -1x * (12 + -1x)) 150 = (240 + -20x + (12 * -1x + -1x * -1x)) 150 = (240 + -20x + (-12x + 1x2)) Combine like terms: -20x + -12x = -32x 150 = (240 + -32x + 1x2) Solving 150 = 240 + -32x + 1x2 Solving for variable 'x'. Combine like terms: 150 + -240 = -90 -90 + 32x + -1x2 = 240 + -32x + 1x2 + -240 + 32x + -1x2 Reorder the terms: -90 + 32x + -1x2 = 240 + -240 + -32x + 32x + 1x2 + -1x2 Combine like terms: 240 + -240 = 0 -90 + 32x + -1x2 = 0 + -32x + 32x + 1x2 + -1x2 -90 + 32x + -1x2 = -32x + 32x + 1x2 + -1x2 Combine like terms: -32x + 32x = 0 -90 + 32x + -1x2 = 0 + 1x2 + -1x2 -90 + 32x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -90 + 32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 90 + -32x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -32x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -32x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -32x + x2 = 0 + -90 -32x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -32x + x2 = -90 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -90 + 256 Reorder the terms: 256 + -32x + x2 = -90 + 256 Combine like terms: -90 + 256 = 166 256 + -32x + x2 = 166 Factor a perfect square on the left side: (x + -16)(x + -16) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + -16) equal to 12.884098727 and -12.884098727.Subproblem 1
x + -16 = 12.884098727 Simplifying x + -16 = 12.884098727 Reorder the terms: -16 + x = 12.884098727 Solving -16 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 12.884098727 + 16 Combine like terms: -16 + 16 = 0 0 + x = 12.884098727 + 16 x = 12.884098727 + 16 Combine like terms: 12.884098727 + 16 = 28.884098727 x = 28.884098727 Simplifying x = 28.884098727Subproblem 2
x + -16 = -12.884098727 Simplifying x + -16 = -12.884098727 Reorder the terms: -16 + x = -12.884098727 Solving -16 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -12.884098727 + 16 Combine like terms: -16 + 16 = 0 0 + x = -12.884098727 + 16 x = -12.884098727 + 16 Combine like terms: -12.884098727 + 16 = 3.115901273 x = 3.115901273 Simplifying x = 3.115901273Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.884098727, 3.115901273}
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