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Simplifying (x + 3)(32 + -1x) = 180 Reorder the terms: (3 + x)(32 + -1x) = 180 Multiply (3 + x) * (32 + -1x) (3(32 + -1x) + x(32 + -1x)) = 180 ((32 * 3 + -1x * 3) + x(32 + -1x)) = 180 ((96 + -3x) + x(32 + -1x)) = 180 (96 + -3x + (32 * x + -1x * x)) = 180 (96 + -3x + (32x + -1x2)) = 180 Combine like terms: -3x + 32x = 29x (96 + 29x + -1x2) = 180 Solving 96 + 29x + -1x2 = 180 Solving for variable 'x'. Reorder the terms: 96 + -180 + 29x + -1x2 = 180 + -180 Combine like terms: 96 + -180 = -84 -84 + 29x + -1x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -84 + 29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 84 + -29x + x2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -29x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -29x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -29x + x2 = 0 + -84 -29x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -29x + x2 = -84 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -84 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -84 + 210.25 Combine like terms: -84 + 210.25 = 126.25 210.25 + -29x + x2 = 126.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + -14.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + -14.5 = 11.236102527 Simplifying x + -14.5 = 11.236102527 Reorder the terms: -14.5 + x = 11.236102527 Solving -14.5 + x = 11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 11.236102527 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 11.236102527 + 14.5 x = 11.236102527 + 14.5 Combine like terms: 11.236102527 + 14.5 = 25.736102527 x = 25.736102527 Simplifying x = 25.736102527Subproblem 2
x + -14.5 = -11.236102527 Simplifying x + -14.5 = -11.236102527 Reorder the terms: -14.5 + x = -11.236102527 Solving -14.5 + x = -11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -11.236102527 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -11.236102527 + 14.5 x = -11.236102527 + 14.5 Combine like terms: -11.236102527 + 14.5 = 3.263897473 x = 3.263897473 Simplifying x = 3.263897473Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.736102527, 3.263897473}
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