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Simplifying (x + -7) + 9 + -1(x + -8)(x + 6) + 57 = 1.09 Reorder the terms: (-7 + x) + 9 + -1(x + -8)(x + 6) + 57 = 1.09 Remove parenthesis around (-7 + x) -7 + x + 9 + -1(x + -8)(x + 6) + 57 = 1.09 Reorder the terms: -7 + x + 9 + -1(-8 + x)(x + 6) + 57 = 1.09 Reorder the terms: -7 + x + 9 + -1(-8 + x)(6 + x) + 57 = 1.09 Multiply (-8 + x) * (6 + x) -7 + x + 9 + -1(-8(6 + x) + x(6 + x)) + 57 = 1.09 -7 + x + 9 + -1((6 * -8 + x * -8) + x(6 + x)) + 57 = 1.09 -7 + x + 9 + -1((-48 + -8x) + x(6 + x)) + 57 = 1.09 -7 + x + 9 + -1(-48 + -8x + (6 * x + x * x)) + 57 = 1.09 -7 + x + 9 + -1(-48 + -8x + (6x + x2)) + 57 = 1.09 Combine like terms: -8x + 6x = -2x -7 + x + 9 + -1(-48 + -2x + x2) + 57 = 1.09 -7 + x + 9 + (-48 * -1 + -2x * -1 + x2 * -1) + 57 = 1.09 -7 + x + 9 + (48 + 2x + -1x2) + 57 = 1.09 Reorder the terms: -7 + 9 + 48 + 57 + x + 2x + -1x2 = 1.09 Combine like terms: -7 + 9 = 2 2 + 48 + 57 + x + 2x + -1x2 = 1.09 Combine like terms: 2 + 48 = 50 50 + 57 + x + 2x + -1x2 = 1.09 Combine like terms: 50 + 57 = 107 107 + x + 2x + -1x2 = 1.09 Combine like terms: x + 2x = 3x 107 + 3x + -1x2 = 1.09 Solving 107 + 3x + -1x2 = 1.09 Solving for variable 'x'. Reorder the terms: 107 + -1.09 + 3x + -1x2 = 1.09 + -1.09 Combine like terms: 107 + -1.09 = 105.91 105.91 + 3x + -1x2 = 1.09 + -1.09 Combine like terms: 1.09 + -1.09 = 0.00 105.91 + 3x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -105.91 + -3x + x2 = 0.00 Move the constant term to the right: Add '105.91' to each side of the equation. -105.91 + -3x + 105.91 + x2 = 0.00 + 105.91 Reorder the terms: -105.91 + 105.91 + -3x + x2 = 0.00 + 105.91 Combine like terms: -105.91 + 105.91 = 0.00 0.00 + -3x + x2 = 0.00 + 105.91 -3x + x2 = 0.00 + 105.91 Combine like terms: 0.00 + 105.91 = 105.91 -3x + x2 = 105.91 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 = 105.91 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 105.91 + 2.25 Combine like terms: 105.91 + 2.25 = 108.16 2.25 + -3x + x2 = 108.16 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 108.16 Calculate the square root of the right side: 10.4 Break this problem into two subproblems by setting (x + -1.5) equal to 10.4 and -10.4.Subproblem 1
x + -1.5 = 10.4 Simplifying x + -1.5 = 10.4 Reorder the terms: -1.5 + x = 10.4 Solving -1.5 + x = 10.4 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 = 10.4 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.4 + 1.5 x = 10.4 + 1.5 Combine like terms: 10.4 + 1.5 = 11.9 x = 11.9 Simplifying x = 11.9Subproblem 2
x + -1.5 = -10.4 Simplifying x + -1.5 = -10.4 Reorder the terms: -1.5 + x = -10.4 Solving -1.5 + x = -10.4 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 = -10.4 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.4 + 1.5 x = -10.4 + 1.5 Combine like terms: -10.4 + 1.5 = -8.9 x = -8.9 Simplifying x = -8.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.9, -8.9}
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