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Simplifying x = (x + 30)(5x + -25) Reorder the terms: x = (30 + x)(5x + -25) Reorder the terms: x = (30 + x)(-25 + 5x) Multiply (30 + x) * (-25 + 5x) x = (30(-25 + 5x) + x(-25 + 5x)) x = ((-25 * 30 + 5x * 30) + x(-25 + 5x)) x = ((-750 + 150x) + x(-25 + 5x)) x = (-750 + 150x + (-25 * x + 5x * x)) x = (-750 + 150x + (-25x + 5x2)) Combine like terms: 150x + -25x = 125x x = (-750 + 125x + 5x2) Solving x = -750 + 125x + 5x2 Solving for variable 'x'. Reorder the terms: 750 + x + -125x + -5x2 = -750 + 125x + 5x2 + 750 + -125x + -5x2 Combine like terms: x + -125x = -124x 750 + -124x + -5x2 = -750 + 125x + 5x2 + 750 + -125x + -5x2 Reorder the terms: 750 + -124x + -5x2 = -750 + 750 + 125x + -125x + 5x2 + -5x2 Combine like terms: -750 + 750 = 0 750 + -124x + -5x2 = 0 + 125x + -125x + 5x2 + -5x2 750 + -124x + -5x2 = 125x + -125x + 5x2 + -5x2 Combine like terms: 125x + -125x = 0 750 + -124x + -5x2 = 0 + 5x2 + -5x2 750 + -124x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 750 + -124x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -150 + 24.8x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 24.8x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 24.8x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 24.8x + x2 = 0 + 150 24.8x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 24.8x + x2 = 150 The x term is 24.8x. Take half its coefficient (12.4). Square it (153.76) and add it to both sides. Add '153.76' to each side of the equation. 24.8x + 153.76 + x2 = 150 + 153.76 Reorder the terms: 153.76 + 24.8x + x2 = 150 + 153.76 Combine like terms: 150 + 153.76 = 303.76 153.76 + 24.8x + x2 = 303.76 Factor a perfect square on the left side: (x + 12.4)(x + 12.4) = 303.76 Calculate the square root of the right side: 17.428711943 Break this problem into two subproblems by setting (x + 12.4) equal to 17.428711943 and -17.428711943.Subproblem 1
x + 12.4 = 17.428711943 Simplifying x + 12.4 = 17.428711943 Reorder the terms: 12.4 + x = 17.428711943 Solving 12.4 + x = 17.428711943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.4' to each side of the equation. 12.4 + -12.4 + x = 17.428711943 + -12.4 Combine like terms: 12.4 + -12.4 = 0.0 0.0 + x = 17.428711943 + -12.4 x = 17.428711943 + -12.4 Combine like terms: 17.428711943 + -12.4 = 5.028711943 x = 5.028711943 Simplifying x = 5.028711943Subproblem 2
x + 12.4 = -17.428711943 Simplifying x + 12.4 = -17.428711943 Reorder the terms: 12.4 + x = -17.428711943 Solving 12.4 + x = -17.428711943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.4' to each side of the equation. 12.4 + -12.4 + x = -17.428711943 + -12.4 Combine like terms: 12.4 + -12.4 = 0.0 0.0 + x = -17.428711943 + -12.4 x = -17.428711943 + -12.4 Combine like terms: -17.428711943 + -12.4 = -29.828711943 x = -29.828711943 Simplifying x = -29.828711943Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.028711943, -29.828711943}
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