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Simplifying 8x + -2x(x + -9) = 2(x + -5) + 1 Reorder the terms: 8x + -2x(-9 + x) = 2(x + -5) + 1 8x + (-9 * -2x + x * -2x) = 2(x + -5) + 1 8x + (18x + -2x2) = 2(x + -5) + 1 Combine like terms: 8x + 18x = 26x 26x + -2x2 = 2(x + -5) + 1 Reorder the terms: 26x + -2x2 = 2(-5 + x) + 1 26x + -2x2 = (-5 * 2 + x * 2) + 1 26x + -2x2 = (-10 + 2x) + 1 Reorder the terms: 26x + -2x2 = -10 + 1 + 2x Combine like terms: -10 + 1 = -9 26x + -2x2 = -9 + 2x Solving 26x + -2x2 = -9 + 2x Solving for variable 'x'. Reorder the terms: 9 + 26x + -2x + -2x2 = -9 + 2x + 9 + -2x Combine like terms: 26x + -2x = 24x 9 + 24x + -2x2 = -9 + 2x + 9 + -2x Reorder the terms: 9 + 24x + -2x2 = -9 + 9 + 2x + -2x Combine like terms: -9 + 9 = 0 9 + 24x + -2x2 = 0 + 2x + -2x 9 + 24x + -2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 9 + 24x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -12x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -12x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -12x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -12x + x2 = 0 + 4.5 -12x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -12x + x2 = 4.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 4.5 + 36 Reorder the terms: 36 + -12x + x2 = 4.5 + 36 Combine like terms: 4.5 + 36 = 40.5 36 + -12x + x2 = 40.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (x + -6) equal to 6.363961031 and -6.363961031.Subproblem 1
x + -6 = 6.363961031 Simplifying x + -6 = 6.363961031 Reorder the terms: -6 + x = 6.363961031 Solving -6 + x = 6.363961031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.363961031 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.363961031 + 6 x = 6.363961031 + 6 Combine like terms: 6.363961031 + 6 = 12.363961031 x = 12.363961031 Simplifying x = 12.363961031Subproblem 2
x + -6 = -6.363961031 Simplifying x + -6 = -6.363961031 Reorder the terms: -6 + x = -6.363961031 Solving -6 + x = -6.363961031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.363961031 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.363961031 + 6 x = -6.363961031 + 6 Combine like terms: -6.363961031 + 6 = -0.363961031 x = -0.363961031 Simplifying x = -0.363961031Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.363961031, -0.363961031}
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