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Simplifying 0.95x + 0.05x(18 + -1x) = 0.10(27) 0.95x + (18 * 0.05x + -1x * 0.05x) = 0.10(27) 0.95x + (0.9x + -0.05x2) = 0.10(27) Combine like terms: 0.95x + 0.9x = 1.85x 1.85x + -0.05x2 = 0.10(27) Multiply 0.10 * 27 1.85x + -0.05x2 = 2.7 Solving 1.85x + -0.05x2 = 2.7 Solving for variable 'x'. Reorder the terms: -2.7 + 1.85x + -0.05x2 = 2.7 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 -2.7 + 1.85x + -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'. 54 + -37x + x2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -37x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -37x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -37x + x2 = 0 + -54 -37x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -37x + x2 = -54 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -54 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -54 + 342.25 Combine like terms: -54 + 342.25 = 288.25 342.25 + -37x + x2 = 288.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (x + -18.5) equal to 16.977926846 and -16.977926846.Subproblem 1
x + -18.5 = 16.977926846 Simplifying x + -18.5 = 16.977926846 Reorder the terms: -18.5 + x = 16.977926846 Solving -18.5 + x = 16.977926846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 16.977926846 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 16.977926846 + 18.5 x = 16.977926846 + 18.5 Combine like terms: 16.977926846 + 18.5 = 35.477926846 x = 35.477926846 Simplifying x = 35.477926846Subproblem 2
x + -18.5 = -16.977926846 Simplifying x + -18.5 = -16.977926846 Reorder the terms: -18.5 + x = -16.977926846 Solving -18.5 + x = -16.977926846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -16.977926846 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -16.977926846 + 18.5 x = -16.977926846 + 18.5 Combine like terms: -16.977926846 + 18.5 = 1.522073154 x = 1.522073154 Simplifying x = 1.522073154Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.477926846, 1.522073154}
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