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Simplifying 8 + -8x + -2x2 = x Solving 8 + -8x + -2x2 = x Solving for variable 'x'. Reorder the terms: 8 + -8x + -1x + -2x2 = x + -1x Combine like terms: -8x + -1x = -9x 8 + -9x + -2x2 = x + -1x Combine like terms: x + -1x = 0 8 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + 4.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.5x + x2 = 0 + 4 4.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.5x + x2 = 4 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 4 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 4 + 5.0625 Combine like terms: 4 + 5.0625 = 9.0625 5.0625 + 4.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 2.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 2.25 = 3.010398645 Simplifying x + 2.25 = 3.010398645 Reorder the terms: 2.25 + x = 3.010398645 Solving 2.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.010398645 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.010398645 + -2.25 x = 3.010398645 + -2.25 Combine like terms: 3.010398645 + -2.25 = 0.760398645 x = 0.760398645 Simplifying x = 0.760398645Subproblem 2
x + 2.25 = -3.010398645 Simplifying x + 2.25 = -3.010398645 Reorder the terms: 2.25 + x = -3.010398645 Solving 2.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.010398645 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.010398645 + -2.25 x = -3.010398645 + -2.25 Combine like terms: -3.010398645 + -2.25 = -5.260398645 x = -5.260398645 Simplifying x = -5.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.760398645, -5.260398645}
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