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Simplifying (x + -4)(2x + -3) = 2x * 2x Reorder the terms: (-4 + x)(2x + -3) = 2x * 2x Reorder the terms: (-4 + x)(-3 + 2x) = 2x * 2x Multiply (-4 + x) * (-3 + 2x) (-4(-3 + 2x) + x(-3 + 2x)) = 2x * 2x ((-3 * -4 + 2x * -4) + x(-3 + 2x)) = 2x * 2x ((12 + -8x) + x(-3 + 2x)) = 2x * 2x (12 + -8x + (-3 * x + 2x * x)) = 2x * 2x (12 + -8x + (-3x + 2x2)) = 2x * 2x Combine like terms: -8x + -3x = -11x (12 + -11x + 2x2) = 2x * 2x Reorder the terms for easier multiplication: 12 + -11x + 2x2 = 2 * 2x * x Multiply 2 * 2 12 + -11x + 2x2 = 4x * x Multiply x * x 12 + -11x + 2x2 = 4x2 Solving 12 + -11x + 2x2 = 4x2 Solving for variable 'x'. Combine like terms: 2x2 + -4x2 = -2x2 12 + -11x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 12 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + 5.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 5.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5.5x + x2 = 0 + 6 5.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 5.5x + x2 = 6 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 = 6 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + 5.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 2.75 = 3.682729966 Simplifying x + 2.75 = 3.682729966 Reorder the terms: 2.75 + x = 3.682729966 Solving 2.75 + x = 3.682729966 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 = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.682729966 + -2.75 x = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 x = 0.932729966 Simplifying x = 0.932729966Subproblem 2
x + 2.75 = -3.682729966 Simplifying x + 2.75 = -3.682729966 Reorder the terms: 2.75 + x = -3.682729966 Solving 2.75 + x = -3.682729966 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 = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.682729966 + -2.75 x = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 x = -6.432729966 Simplifying x = -6.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932729966, -6.432729966}
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