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Simplifying 3(x + -5) + -4(2x + -4) = -2x(x + -11) Reorder the terms: 3(-5 + x) + -4(2x + -4) = -2x(x + -11) (-5 * 3 + x * 3) + -4(2x + -4) = -2x(x + -11) (-15 + 3x) + -4(2x + -4) = -2x(x + -11) Reorder the terms: -15 + 3x + -4(-4 + 2x) = -2x(x + -11) -15 + 3x + (-4 * -4 + 2x * -4) = -2x(x + -11) -15 + 3x + (16 + -8x) = -2x(x + -11) Reorder the terms: -15 + 16 + 3x + -8x = -2x(x + -11) Combine like terms: -15 + 16 = 1 1 + 3x + -8x = -2x(x + -11) Combine like terms: 3x + -8x = -5x 1 + -5x = -2x(x + -11) Reorder the terms: 1 + -5x = -2x(-11 + x) 1 + -5x = (-11 * -2x + x * -2x) 1 + -5x = (22x + -2x2) Solving 1 + -5x = 22x + -2x2 Solving for variable 'x'. Combine like terms: -5x + -22x = -27x 1 + -27x + 2x2 = 22x + -2x2 + -22x + 2x2 Reorder the terms: 1 + -27x + 2x2 = 22x + -22x + -2x2 + 2x2 Combine like terms: 22x + -22x = 0 1 + -27x + 2x2 = 0 + -2x2 + 2x2 1 + -27x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 1 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -13.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -13.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -13.5x + x2 = 0 + -0.5 -13.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -13.5x + x2 = -0.5 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -0.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -0.5 + 45.5625 Combine like terms: -0.5 + 45.5625 = 45.0625 45.5625 + -13.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + -6.75) equal to 6.712860791 and -6.712860791.Subproblem 1
x + -6.75 = 6.712860791 Simplifying x + -6.75 = 6.712860791 Reorder the terms: -6.75 + x = 6.712860791 Solving -6.75 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 6.712860791 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 6.712860791 + 6.75 x = 6.712860791 + 6.75 Combine like terms: 6.712860791 + 6.75 = 13.462860791 x = 13.462860791 Simplifying x = 13.462860791Subproblem 2
x + -6.75 = -6.712860791 Simplifying x + -6.75 = -6.712860791 Reorder the terms: -6.75 + x = -6.712860791 Solving -6.75 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -6.712860791 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -6.712860791 + 6.75 x = -6.712860791 + 6.75 Combine like terms: -6.712860791 + 6.75 = 0.037139209 x = 0.037139209 Simplifying x = 0.037139209Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.462860791, 0.037139209}
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