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Simplifying 4(x + -6) * x = 5(x + -7) + 11 Reorder the terms: 4(-6 + x) * x = 5(x + -7) + 11 Reorder the terms for easier multiplication: 4x(-6 + x) = 5(x + -7) + 11 (-6 * 4x + x * 4x) = 5(x + -7) + 11 (-24x + 4x2) = 5(x + -7) + 11 Reorder the terms: -24x + 4x2 = 5(-7 + x) + 11 -24x + 4x2 = (-7 * 5 + x * 5) + 11 -24x + 4x2 = (-35 + 5x) + 11 Reorder the terms: -24x + 4x2 = -35 + 11 + 5x Combine like terms: -35 + 11 = -24 -24x + 4x2 = -24 + 5x Solving -24x + 4x2 = -24 + 5x Solving for variable 'x'. Reorder the terms: 24 + -24x + -5x + 4x2 = -24 + 5x + 24 + -5x Combine like terms: -24x + -5x = -29x 24 + -29x + 4x2 = -24 + 5x + 24 + -5x Reorder the terms: 24 + -29x + 4x2 = -24 + 24 + 5x + -5x Combine like terms: -24 + 24 = 0 24 + -29x + 4x2 = 0 + 5x + -5x 24 + -29x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 24 + -29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + -7.25x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -7.25x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -7.25x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7.25x + x2 = 0 + -6 -7.25x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -7.25x + x2 = -6 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -6 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -6 + 13.140625 Combine like terms: -6 + 13.140625 = 7.140625 13.140625 + -7.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -3.625) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -3.625 = 2.672194791 Simplifying x + -3.625 = 2.672194791 Reorder the terms: -3.625 + x = 2.672194791 Solving -3.625 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 2.672194791 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 2.672194791 + 3.625 x = 2.672194791 + 3.625 Combine like terms: 2.672194791 + 3.625 = 6.297194791 x = 6.297194791 Simplifying x = 6.297194791Subproblem 2
x + -3.625 = -2.672194791 Simplifying x + -3.625 = -2.672194791 Reorder the terms: -3.625 + x = -2.672194791 Solving -3.625 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -2.672194791 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -2.672194791 + 3.625 x = -2.672194791 + 3.625 Combine like terms: -2.672194791 + 3.625 = 0.952805209 x = 0.952805209 Simplifying x = 0.952805209Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.297194791, 0.952805209}
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