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Simplifying x + 2x(x + -5) = 135 Reorder the terms: x + 2x(-5 + x) = 135 x + (-5 * 2x + x * 2x) = 135 x + (-10x + 2x2) = 135 Combine like terms: x + -10x = -9x -9x + 2x2 = 135 Solving -9x + 2x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + -9x + 2x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -67.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + -4.5x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + -4.5x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + -4.5x + x2 = 0 + 67.5 -4.5x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 -4.5x + x2 = 67.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 67.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 67.5 + 5.0625 Combine like terms: 67.5 + 5.0625 = 72.5625 5.0625 + -4.5x + x2 = 72.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (x + -2.25) equal to 8.518362519 and -8.518362519.Subproblem 1
x + -2.25 = 8.518362519 Simplifying x + -2.25 = 8.518362519 Reorder the terms: -2.25 + x = 8.518362519 Solving -2.25 + x = 8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 8.518362519 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 8.518362519 + 2.25 x = 8.518362519 + 2.25 Combine like terms: 8.518362519 + 2.25 = 10.768362519 x = 10.768362519 Simplifying x = 10.768362519Subproblem 2
x + -2.25 = -8.518362519 Simplifying x + -2.25 = -8.518362519 Reorder the terms: -2.25 + x = -8.518362519 Solving -2.25 + x = -8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -8.518362519 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -8.518362519 + 2.25 x = -8.518362519 + 2.25 Combine like terms: -8.518362519 + 2.25 = -6.268362519 x = -6.268362519 Simplifying x = -6.268362519Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.768362519, -6.268362519}
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