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Simplifying (x + 7) + -1(2x + -4)(x + 5) = 0 Reorder the terms: (7 + x) + -1(2x + -4)(x + 5) = 0 Remove parenthesis around (7 + x) 7 + x + -1(2x + -4)(x + 5) = 0 Reorder the terms: 7 + x + -1(-4 + 2x)(x + 5) = 0 Reorder the terms: 7 + x + -1(-4 + 2x)(5 + x) = 0 Multiply (-4 + 2x) * (5 + x) 7 + x + -1(-4(5 + x) + 2x * (5 + x)) = 0 7 + x + -1((5 * -4 + x * -4) + 2x * (5 + x)) = 0 7 + x + -1((-20 + -4x) + 2x * (5 + x)) = 0 7 + x + -1(-20 + -4x + (5 * 2x + x * 2x)) = 0 7 + x + -1(-20 + -4x + (10x + 2x2)) = 0 Combine like terms: -4x + 10x = 6x 7 + x + -1(-20 + 6x + 2x2) = 0 7 + x + (-20 * -1 + 6x * -1 + 2x2 * -1) = 0 7 + x + (20 + -6x + -2x2) = 0 Reorder the terms: 7 + 20 + x + -6x + -2x2 = 0 Combine like terms: 7 + 20 = 27 27 + x + -6x + -2x2 = 0 Combine like terms: x + -6x = -5x 27 + -5x + -2x2 = 0 Solving 27 + -5x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 2.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 2.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 2.5x + x2 = 0 + 13.5 2.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 2.5x + x2 = 13.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 13.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 13.5 + 1.5625 Combine like terms: 13.5 + 1.5625 = 15.0625 1.5625 + 2.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 1.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 1.25 = 3.881043674 Simplifying x + 1.25 = 3.881043674 Reorder the terms: 1.25 + x = 3.881043674 Solving 1.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.881043674 + -1.25 x = 3.881043674 + -1.25 Combine like terms: 3.881043674 + -1.25 = 2.631043674 x = 2.631043674 Simplifying x = 2.631043674Subproblem 2
x + 1.25 = -3.881043674 Simplifying x + 1.25 = -3.881043674 Reorder the terms: 1.25 + x = -3.881043674 Solving 1.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.881043674 + -1.25 x = -3.881043674 + -1.25 Combine like terms: -3.881043674 + -1.25 = -5.131043674 x = -5.131043674 Simplifying x = -5.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.631043674, -5.131043674}
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