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Simplifying (x + -3)(2x + -5) = 12 Reorder the terms: (-3 + x)(2x + -5) = 12 Reorder the terms: (-3 + x)(-5 + 2x) = 12 Multiply (-3 + x) * (-5 + 2x) (-3(-5 + 2x) + x(-5 + 2x)) = 12 ((-5 * -3 + 2x * -3) + x(-5 + 2x)) = 12 ((15 + -6x) + x(-5 + 2x)) = 12 (15 + -6x + (-5 * x + 2x * x)) = 12 (15 + -6x + (-5x + 2x2)) = 12 Combine like terms: -6x + -5x = -11x (15 + -11x + 2x2) = 12 Solving 15 + -11x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: 15 + -12 + -11x + 2x2 = 12 + -12 Combine like terms: 15 + -12 = 3 3 + -11x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 3 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5.5x + x2 = 0 + -1.5 -5.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5.5x + x2 = -1.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1.5 + 7.5625 Combine like terms: -1.5 + 7.5625 = 6.0625 7.5625 + -5.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -2.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -2.75 = 2.46221445 Simplifying x + -2.75 = 2.46221445 Reorder the terms: -2.75 + x = 2.46221445 Solving -2.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.46221445 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.46221445 + 2.75 x = 2.46221445 + 2.75 Combine like terms: 2.46221445 + 2.75 = 5.21221445 x = 5.21221445 Simplifying x = 5.21221445Subproblem 2
x + -2.75 = -2.46221445 Simplifying x + -2.75 = -2.46221445 Reorder the terms: -2.75 + x = -2.46221445 Solving -2.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.46221445 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.46221445 + 2.75 x = -2.46221445 + 2.75 Combine like terms: -2.46221445 + 2.75 = 0.28778555 x = 0.28778555 Simplifying x = 0.28778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.21221445, 0.28778555}
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