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Simplifying (x + -5)(x + -6) = 2x + -3 Reorder the terms: (-5 + x)(x + -6) = 2x + -3 Reorder the terms: (-5 + x)(-6 + x) = 2x + -3 Multiply (-5 + x) * (-6 + x) (-5(-6 + x) + x(-6 + x)) = 2x + -3 ((-6 * -5 + x * -5) + x(-6 + x)) = 2x + -3 ((30 + -5x) + x(-6 + x)) = 2x + -3 (30 + -5x + (-6 * x + x * x)) = 2x + -3 (30 + -5x + (-6x + x2)) = 2x + -3 Combine like terms: -5x + -6x = -11x (30 + -11x + x2) = 2x + -3 Reorder the terms: 30 + -11x + x2 = -3 + 2x Solving 30 + -11x + x2 = -3 + 2x Solving for variable 'x'. Reorder the terms: 30 + 3 + -11x + -2x + x2 = -3 + 2x + 3 + -2x Combine like terms: 30 + 3 = 33 33 + -11x + -2x + x2 = -3 + 2x + 3 + -2x Combine like terms: -11x + -2x = -13x 33 + -13x + x2 = -3 + 2x + 3 + -2x Reorder the terms: 33 + -13x + x2 = -3 + 3 + 2x + -2x Combine like terms: -3 + 3 = 0 33 + -13x + x2 = 0 + 2x + -2x 33 + -13x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 33 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -13x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + -13x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -13x + x2 = 0 + -33 -13x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 -13x + x2 = -33 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -33 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -33 + 42.25 Combine like terms: -33 + 42.25 = 9.25 42.25 + -13x + x2 = 9.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -6.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -6.5 = 3.041381265 Simplifying x + -6.5 = 3.041381265 Reorder the terms: -6.5 + x = 3.041381265 Solving -6.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 3.041381265 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.041381265 + 6.5 x = 3.041381265 + 6.5 Combine like terms: 3.041381265 + 6.5 = 9.541381265 x = 9.541381265 Simplifying x = 9.541381265Subproblem 2
x + -6.5 = -3.041381265 Simplifying x + -6.5 = -3.041381265 Reorder the terms: -6.5 + x = -3.041381265 Solving -6.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -3.041381265 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.041381265 + 6.5 x = -3.041381265 + 6.5 Combine like terms: -3.041381265 + 6.5 = 3.458618735 x = 3.458618735 Simplifying x = 3.458618735Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.541381265, 3.458618735}
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