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Simplifying 0.12x + 0.6x(24 + -1x) = 0.09(24) 0.12x + (24 * 0.6x + -1x * 0.6x) = 0.09(24) 0.12x + (14.4x + -0.6x2) = 0.09(24) Combine like terms: 0.12x + 14.4x = 14.52x 14.52x + -0.6x2 = 0.09(24) Multiply 0.09 * 24 14.52x + -0.6x2 = 2.16 Solving 14.52x + -0.6x2 = 2.16 Solving for variable 'x'. Reorder the terms: -2.16 + 14.52x + -0.6x2 = 2.16 + -2.16 Combine like terms: 2.16 + -2.16 = 0.00 -2.16 + 14.52x + -0.6x2 = 0.00 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 3.6 + -24.2x + x2 = 0.0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -24.2x + -3.6 + x2 = 0.0 + -3.6 Reorder the terms: 3.6 + -3.6 + -24.2x + x2 = 0.0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -24.2x + x2 = 0.0 + -3.6 -24.2x + x2 = 0.0 + -3.6 Combine like terms: 0.0 + -3.6 = -3.6 -24.2x + x2 = -3.6 The x term is -24.2x. Take half its coefficient (-12.1). Square it (146.41) and add it to both sides. Add '146.41' to each side of the equation. -24.2x + 146.41 + x2 = -3.6 + 146.41 Reorder the terms: 146.41 + -24.2x + x2 = -3.6 + 146.41 Combine like terms: -3.6 + 146.41 = 142.81 146.41 + -24.2x + x2 = 142.81 Factor a perfect square on the left side: (x + -12.1)(x + -12.1) = 142.81 Calculate the square root of the right side: 11.950313803 Break this problem into two subproblems by setting (x + -12.1) equal to 11.950313803 and -11.950313803.Subproblem 1
x + -12.1 = 11.950313803 Simplifying x + -12.1 = 11.950313803 Reorder the terms: -12.1 + x = 11.950313803 Solving -12.1 + x = 11.950313803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.1' to each side of the equation. -12.1 + 12.1 + x = 11.950313803 + 12.1 Combine like terms: -12.1 + 12.1 = 0.0 0.0 + x = 11.950313803 + 12.1 x = 11.950313803 + 12.1 Combine like terms: 11.950313803 + 12.1 = 24.050313803 x = 24.050313803 Simplifying x = 24.050313803Subproblem 2
x + -12.1 = -11.950313803 Simplifying x + -12.1 = -11.950313803 Reorder the terms: -12.1 + x = -11.950313803 Solving -12.1 + x = -11.950313803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.1' to each side of the equation. -12.1 + 12.1 + x = -11.950313803 + 12.1 Combine like terms: -12.1 + 12.1 = 0.0 0.0 + x = -11.950313803 + 12.1 x = -11.950313803 + 12.1 Combine like terms: -11.950313803 + 12.1 = 0.149686197 x = 0.149686197 Simplifying x = 0.149686197Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.050313803, 0.149686197}
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