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Simplifying 5x(16 + -1x) = 72 (16 * 5x + -1x * 5x) = 72 (80x + -5x2) = 72 Solving 80x + -5x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + 80x + -5x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 80x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 14.4 + -16x + x2 = 0 Move the constant term to the right: Add '-14.4' to each side of the equation. 14.4 + -16x + -14.4 + x2 = 0 + -14.4 Reorder the terms: 14.4 + -14.4 + -16x + x2 = 0 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + -16x + x2 = 0 + -14.4 -16x + x2 = 0 + -14.4 Combine like terms: 0 + -14.4 = -14.4 -16x + x2 = -14.4 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -14.4 + 64 Reorder the terms: 64 + -16x + x2 = -14.4 + 64 Combine like terms: -14.4 + 64 = 49.6 64 + -16x + x2 = 49.6 Factor a perfect square on the left side: (x + -8)(x + -8) = 49.6 Calculate the square root of the right side: 7.042726745 Break this problem into two subproblems by setting (x + -8) equal to 7.042726745 and -7.042726745.Subproblem 1
x + -8 = 7.042726745 Simplifying x + -8 = 7.042726745 Reorder the terms: -8 + x = 7.042726745 Solving -8 + x = 7.042726745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.042726745 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.042726745 + 8 x = 7.042726745 + 8 Combine like terms: 7.042726745 + 8 = 15.042726745 x = 15.042726745 Simplifying x = 15.042726745Subproblem 2
x + -8 = -7.042726745 Simplifying x + -8 = -7.042726745 Reorder the terms: -8 + x = -7.042726745 Solving -8 + x = -7.042726745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.042726745 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.042726745 + 8 x = -7.042726745 + 8 Combine like terms: -7.042726745 + 8 = 0.957273255 x = 0.957273255 Simplifying x = 0.957273255Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.042726745, 0.957273255}
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