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Simplifying 16 + 0.08x = 0.1x(100 + x) 16 + 0.08x = (100 * 0.1x + x * 0.1x) 16 + 0.08x = (10x + 0.1x2) Solving 16 + 0.08x = 10x + 0.1x2 Solving for variable 'x'. Combine like terms: 0.08x + -10x = -9.92x 16 + -9.92x + -0.1x2 = 10x + 0.1x2 + -10x + -0.1x2 Reorder the terms: 16 + -9.92x + -0.1x2 = 10x + -10x + 0.1x2 + -0.1x2 Combine like terms: 10x + -10x = 0 16 + -9.92x + -0.1x2 = 0 + 0.1x2 + -0.1x2 16 + -9.92x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 16 + -9.92x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -160 + 99.2x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 99.2x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 99.2x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 99.2x + x2 = 0 + 160 99.2x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 99.2x + x2 = 160 The x term is 99.2x. Take half its coefficient (49.6). Square it (2460.16) and add it to both sides. Add '2460.16' to each side of the equation. 99.2x + 2460.16 + x2 = 160 + 2460.16 Reorder the terms: 2460.16 + 99.2x + x2 = 160 + 2460.16 Combine like terms: 160 + 2460.16 = 2620.16 2460.16 + 99.2x + x2 = 2620.16 Factor a perfect square on the left side: (x + 49.6)(x + 49.6) = 2620.16 Calculate the square root of the right side: 51.187498474 Break this problem into two subproblems by setting (x + 49.6) equal to 51.187498474 and -51.187498474.Subproblem 1
x + 49.6 = 51.187498474 Simplifying x + 49.6 = 51.187498474 Reorder the terms: 49.6 + x = 51.187498474 Solving 49.6 + x = 51.187498474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49.6' to each side of the equation. 49.6 + -49.6 + x = 51.187498474 + -49.6 Combine like terms: 49.6 + -49.6 = 0.0 0.0 + x = 51.187498474 + -49.6 x = 51.187498474 + -49.6 Combine like terms: 51.187498474 + -49.6 = 1.587498474 x = 1.587498474 Simplifying x = 1.587498474Subproblem 2
x + 49.6 = -51.187498474 Simplifying x + 49.6 = -51.187498474 Reorder the terms: 49.6 + x = -51.187498474 Solving 49.6 + x = -51.187498474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49.6' to each side of the equation. 49.6 + -49.6 + x = -51.187498474 + -49.6 Combine like terms: 49.6 + -49.6 = 0.0 0.0 + x = -51.187498474 + -49.6 x = -51.187498474 + -49.6 Combine like terms: -51.187498474 + -49.6 = -100.787498474 x = -100.787498474 Simplifying x = -100.787498474Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.587498474, -100.787498474}
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