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Simplifying 1.00x + 0.05x(12 + -1x) = 0.10(63) 1.00x + (12 * 0.05x + -1x * 0.05x) = 0.10(63) 1.00x + (0.6x + -0.05x2) = 0.10(63) Combine like terms: 1.00x + 0.6x = 1.6x 1.6x + -0.05x2 = 0.10(63) Multiply 0.10 * 63 1.6x + -0.05x2 = 6.3 Solving 1.6x + -0.05x2 = 6.3 Solving for variable 'x'. Reorder the terms: -6.3 + 1.6x + -0.05x2 = 6.3 + -6.3 Combine like terms: 6.3 + -6.3 = 0.0 -6.3 + 1.6x + -0.05x2 = 0.0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 126 + -32x + x2 = 0 Move the constant term to the right: Add '-126' to each side of the equation. 126 + -32x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + -32x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -32x + x2 = 0 + -126 -32x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 -32x + x2 = -126 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 = -126 + 256 Reorder the terms: 256 + -32x + x2 = -126 + 256 Combine like terms: -126 + 256 = 130 256 + -32x + x2 = 130 Factor a perfect square on the left side: (x + -16)(x + -16) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + -16) equal to 11.401754251 and -11.401754251.Subproblem 1
x + -16 = 11.401754251 Simplifying x + -16 = 11.401754251 Reorder the terms: -16 + x = 11.401754251 Solving -16 + x = 11.401754251 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 = 11.401754251 + 16 Combine like terms: -16 + 16 = 0 0 + x = 11.401754251 + 16 x = 11.401754251 + 16 Combine like terms: 11.401754251 + 16 = 27.401754251 x = 27.401754251 Simplifying x = 27.401754251Subproblem 2
x + -16 = -11.401754251 Simplifying x + -16 = -11.401754251 Reorder the terms: -16 + x = -11.401754251 Solving -16 + x = -11.401754251 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 = -11.401754251 + 16 Combine like terms: -16 + 16 = 0 0 + x = -11.401754251 + 16 x = -11.401754251 + 16 Combine like terms: -11.401754251 + 16 = 4.598245749 x = 4.598245749 Simplifying x = 4.598245749Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.401754251, 4.598245749}
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