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Simplifying 8x + -8 + 8x = x2 + -1x Reorder the terms: -8 + 8x + 8x = x2 + -1x Combine like terms: 8x + 8x = 16x -8 + 16x = x2 + -1x Reorder the terms: -8 + 16x = -1x + x2 Solving -8 + 16x = -1x + x2 Solving for variable 'x'. Combine like terms: 16x + x = 17x -8 + 17x + -1x2 = -1x + x2 + x + -1x2 Reorder the terms: -8 + 17x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 -8 + 17x + -1x2 = 0 + x2 + -1x2 -8 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -17x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -17x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -17x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -17x + x2 = 0 + -8 -17x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -17x + x2 = -8 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -8 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -8 + 72.25 Combine like terms: -8 + 72.25 = 64.25 72.25 + -17x + x2 = 64.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -8.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + -8.5 = 8.015609771 Simplifying x + -8.5 = 8.015609771 Reorder the terms: -8.5 + x = 8.015609771 Solving -8.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.015609771 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.015609771 + 8.5 x = 8.015609771 + 8.5 Combine like terms: 8.015609771 + 8.5 = 16.515609771 x = 16.515609771 Simplifying x = 16.515609771Subproblem 2
x + -8.5 = -8.015609771 Simplifying x + -8.5 = -8.015609771 Reorder the terms: -8.5 + x = -8.015609771 Solving -8.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.015609771 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.015609771 + 8.5 x = -8.015609771 + 8.5 Combine like terms: -8.015609771 + 8.5 = 0.484390229 x = 0.484390229 Simplifying x = 0.484390229Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.515609771, 0.484390229}
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