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Simplifying 0.3x + 0.05x(18 + -1x) = 0.10(-31) 0.3x + (18 * 0.05x + -1x * 0.05x) = 0.10(-31) 0.3x + (0.9x + -0.05x2) = 0.10(-31) Combine like terms: 0.3x + 0.9x = 1.2x 1.2x + -0.05x2 = 0.10(-31) Multiply 0.10 * -31 1.2x + -0.05x2 = -3.1 Solving 1.2x + -0.05x2 = -3.1 Solving for variable 'x'. Reorder the terms: 3.1 + 1.2x + -0.05x2 = -3.1 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 3.1 + 1.2x + -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'. -62 + -24x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -24x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -24x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -24x + x2 = 0 + 62 -24x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -24x + x2 = 62 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 62 + 144 Reorder the terms: 144 + -24x + x2 = 62 + 144 Combine like terms: 62 + 144 = 206 144 + -24x + x2 = 206 Factor a perfect square on the left side: (x + -12)(x + -12) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + -12) equal to 14.352700094 and -14.352700094.Subproblem 1
x + -12 = 14.352700094 Simplifying x + -12 = 14.352700094 Reorder the terms: -12 + x = 14.352700094 Solving -12 + x = 14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 14.352700094 + 12 Combine like terms: -12 + 12 = 0 0 + x = 14.352700094 + 12 x = 14.352700094 + 12 Combine like terms: 14.352700094 + 12 = 26.352700094 x = 26.352700094 Simplifying x = 26.352700094Subproblem 2
x + -12 = -14.352700094 Simplifying x + -12 = -14.352700094 Reorder the terms: -12 + x = -14.352700094 Solving -12 + x = -14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -14.352700094 + 12 Combine like terms: -12 + 12 = 0 0 + x = -14.352700094 + 12 x = -14.352700094 + 12 Combine like terms: -14.352700094 + 12 = -2.352700094 x = -2.352700094 Simplifying x = -2.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.352700094, -2.352700094}
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