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Simplifying (x + -7)(2x + -11) = 150 Reorder the terms: (-7 + x)(2x + -11) = 150 Reorder the terms: (-7 + x)(-11 + 2x) = 150 Multiply (-7 + x) * (-11 + 2x) (-7(-11 + 2x) + x(-11 + 2x)) = 150 ((-11 * -7 + 2x * -7) + x(-11 + 2x)) = 150 ((77 + -14x) + x(-11 + 2x)) = 150 (77 + -14x + (-11 * x + 2x * x)) = 150 (77 + -14x + (-11x + 2x2)) = 150 Combine like terms: -14x + -11x = -25x (77 + -25x + 2x2) = 150 Solving 77 + -25x + 2x2 = 150 Solving for variable 'x'. Reorder the terms: 77 + -150 + -25x + 2x2 = 150 + -150 Combine like terms: 77 + -150 = -73 -73 + -25x + 2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -73 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + -12.5x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + -12.5x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + -12.5x + x2 = 0 + 36.5 -12.5x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 -12.5x + x2 = 36.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 36.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 36.5 + 39.0625 Combine like terms: 36.5 + 39.0625 = 75.5625 39.0625 + -12.5x + x2 = 75.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 75.5625 Calculate the square root of the right side: 8.692669325 Break this problem into two subproblems by setting (x + -6.25) equal to 8.692669325 and -8.692669325.Subproblem 1
x + -6.25 = 8.692669325 Simplifying x + -6.25 = 8.692669325 Reorder the terms: -6.25 + x = 8.692669325 Solving -6.25 + x = 8.692669325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 8.692669325 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 8.692669325 + 6.25 x = 8.692669325 + 6.25 Combine like terms: 8.692669325 + 6.25 = 14.942669325 x = 14.942669325 Simplifying x = 14.942669325Subproblem 2
x + -6.25 = -8.692669325 Simplifying x + -6.25 = -8.692669325 Reorder the terms: -6.25 + x = -8.692669325 Solving -6.25 + x = -8.692669325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -8.692669325 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -8.692669325 + 6.25 x = -8.692669325 + 6.25 Combine like terms: -8.692669325 + 6.25 = -2.442669325 x = -2.442669325 Simplifying x = -2.442669325Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.942669325, -2.442669325}
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