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Simplifying (2x + 3)(x + -6) = 90 Reorder the terms: (3 + 2x)(x + -6) = 90 Reorder the terms: (3 + 2x)(-6 + x) = 90 Multiply (3 + 2x) * (-6 + x) (3(-6 + x) + 2x * (-6 + x)) = 90 ((-6 * 3 + x * 3) + 2x * (-6 + x)) = 90 ((-18 + 3x) + 2x * (-6 + x)) = 90 (-18 + 3x + (-6 * 2x + x * 2x)) = 90 (-18 + 3x + (-12x + 2x2)) = 90 Combine like terms: 3x + -12x = -9x (-18 + -9x + 2x2) = 90 Solving -18 + -9x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -18 + -90 + -9x + 2x2 = 90 + -90 Combine like terms: -18 + -90 = -108 -108 + -9x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -108 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -54 + -4.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -4.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -4.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -4.5x + x2 = 0 + 54 -4.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -4.5x + x2 = 54 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 = 54 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 54 + 5.0625 Combine like terms: 54 + 5.0625 = 59.0625 5.0625 + -4.5x + x2 = 59.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 59.0625 Calculate the square root of the right side: 7.685213074 Break this problem into two subproblems by setting (x + -2.25) equal to 7.685213074 and -7.685213074.Subproblem 1
x + -2.25 = 7.685213074 Simplifying x + -2.25 = 7.685213074 Reorder the terms: -2.25 + x = 7.685213074 Solving -2.25 + x = 7.685213074 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 = 7.685213074 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.685213074 + 2.25 x = 7.685213074 + 2.25 Combine like terms: 7.685213074 + 2.25 = 9.935213074 x = 9.935213074 Simplifying x = 9.935213074Subproblem 2
x + -2.25 = -7.685213074 Simplifying x + -2.25 = -7.685213074 Reorder the terms: -2.25 + x = -7.685213074 Solving -2.25 + x = -7.685213074 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 = -7.685213074 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.685213074 + 2.25 x = -7.685213074 + 2.25 Combine like terms: -7.685213074 + 2.25 = -5.435213074 x = -5.435213074 Simplifying x = -5.435213074Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.935213074, -5.435213074}
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