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Simplifying 7x + 5x(24 + -1x) = 147 7x + (24 * 5x + -1x * 5x) = 147 7x + (120x + -5x2) = 147 Combine like terms: 7x + 120x = 127x 127x + -5x2 = 147 Solving 127x + -5x2 = 147 Solving for variable 'x'. Reorder the terms: -147 + 127x + -5x2 = 147 + -147 Combine like terms: 147 + -147 = 0 -147 + 127x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 29.4 + -25.4x + x2 = 0 Move the constant term to the right: Add '-29.4' to each side of the equation. 29.4 + -25.4x + -29.4 + x2 = 0 + -29.4 Reorder the terms: 29.4 + -29.4 + -25.4x + x2 = 0 + -29.4 Combine like terms: 29.4 + -29.4 = 0.0 0.0 + -25.4x + x2 = 0 + -29.4 -25.4x + x2 = 0 + -29.4 Combine like terms: 0 + -29.4 = -29.4 -25.4x + x2 = -29.4 The x term is -25.4x. Take half its coefficient (-12.7). Square it (161.29) and add it to both sides. Add '161.29' to each side of the equation. -25.4x + 161.29 + x2 = -29.4 + 161.29 Reorder the terms: 161.29 + -25.4x + x2 = -29.4 + 161.29 Combine like terms: -29.4 + 161.29 = 131.89 161.29 + -25.4x + x2 = 131.89 Factor a perfect square on the left side: (x + -12.7)(x + -12.7) = 131.89 Calculate the square root of the right side: 11.48433716 Break this problem into two subproblems by setting (x + -12.7) equal to 11.48433716 and -11.48433716.Subproblem 1
x + -12.7 = 11.48433716 Simplifying x + -12.7 = 11.48433716 Reorder the terms: -12.7 + x = 11.48433716 Solving -12.7 + x = 11.48433716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.7' to each side of the equation. -12.7 + 12.7 + x = 11.48433716 + 12.7 Combine like terms: -12.7 + 12.7 = 0.0 0.0 + x = 11.48433716 + 12.7 x = 11.48433716 + 12.7 Combine like terms: 11.48433716 + 12.7 = 24.18433716 x = 24.18433716 Simplifying x = 24.18433716Subproblem 2
x + -12.7 = -11.48433716 Simplifying x + -12.7 = -11.48433716 Reorder the terms: -12.7 + x = -11.48433716 Solving -12.7 + x = -11.48433716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.7' to each side of the equation. -12.7 + 12.7 + x = -11.48433716 + 12.7 Combine like terms: -12.7 + 12.7 = 0.0 0.0 + x = -11.48433716 + 12.7 x = -11.48433716 + 12.7 Combine like terms: -11.48433716 + 12.7 = 1.21566284 x = 1.21566284 Simplifying x = 1.21566284Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.18433716, 1.21566284}
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