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Simplifying (2x + -3)(2x + -3) = 56 Reorder the terms: (-3 + 2x)(2x + -3) = 56 Reorder the terms: (-3 + 2x)(-3 + 2x) = 56 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) = 56 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 56 ((9 + -6x) + 2x * (-3 + 2x)) = 56 (9 + -6x + (-3 * 2x + 2x * 2x)) = 56 (9 + -6x + (-6x + 4x2)) = 56 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) = 56 Solving 9 + -12x + 4x2 = 56 Solving for variable 'x'. Reorder the terms: 9 + -56 + -12x + 4x2 = 56 + -56 Combine like terms: 9 + -56 = -47 -47 + -12x + 4x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -47 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.75 + -3x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + -3x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + -3x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + -3x + x2 = 0 + 11.75 -3x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 -3x + x2 = 11.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 11.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 11.75 + 2.25 Combine like terms: 11.75 + 2.25 = 14 2.25 + -3x + x2 = 14 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -1.5) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -1.5 = 3.741657387 Simplifying x + -1.5 = 3.741657387 Reorder the terms: -1.5 + x = 3.741657387 Solving -1.5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.741657387 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.741657387 + 1.5 x = 3.741657387 + 1.5 Combine like terms: 3.741657387 + 1.5 = 5.241657387 x = 5.241657387 Simplifying x = 5.241657387Subproblem 2
x + -1.5 = -3.741657387 Simplifying x + -1.5 = -3.741657387 Reorder the terms: -1.5 + x = -3.741657387 Solving -1.5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.741657387 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.741657387 + 1.5 x = -3.741657387 + 1.5 Combine like terms: -3.741657387 + 1.5 = -2.241657387 x = -2.241657387 Simplifying x = -2.241657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.241657387, -2.241657387}
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