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Simplifying 8x2 + -91 = -16x + -6 Reorder the terms: -91 + 8x2 = -16x + -6 Reorder the terms: -91 + 8x2 = -6 + -16x Solving -91 + 8x2 = -6 + -16x Solving for variable 'x'. Reorder the terms: -91 + 6 + 16x + 8x2 = -6 + -16x + 6 + 16x Combine like terms: -91 + 6 = -85 -85 + 16x + 8x2 = -6 + -16x + 6 + 16x Reorder the terms: -85 + 16x + 8x2 = -6 + 6 + -16x + 16x Combine like terms: -6 + 6 = 0 -85 + 16x + 8x2 = 0 + -16x + 16x -85 + 16x + 8x2 = -16x + 16x Combine like terms: -16x + 16x = 0 -85 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10.625 + 2x + x2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + 2x + 10.625 + x2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + 2x + x2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + 2x + x2 = 0 + 10.625 2x + x2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 2x + x2 = 10.625 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10.625 + 1 Reorder the terms: 1 + 2x + x2 = 10.625 + 1 Combine like terms: 10.625 + 1 = 11.625 1 + 2x + x2 = 11.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 11.625 Calculate the square root of the right side: 3.409545424 Break this problem into two subproblems by setting (x + 1) equal to 3.409545424 and -3.409545424.Subproblem 1
x + 1 = 3.409545424 Simplifying x + 1 = 3.409545424 Reorder the terms: 1 + x = 3.409545424 Solving 1 + x = 3.409545424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.409545424 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.409545424 + -1 x = 3.409545424 + -1 Combine like terms: 3.409545424 + -1 = 2.409545424 x = 2.409545424 Simplifying x = 2.409545424Subproblem 2
x + 1 = -3.409545424 Simplifying x + 1 = -3.409545424 Reorder the terms: 1 + x = -3.409545424 Solving 1 + x = -3.409545424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.409545424 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.409545424 + -1 x = -3.409545424 + -1 Combine like terms: -3.409545424 + -1 = -4.409545424 x = -4.409545424 Simplifying x = -4.409545424Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.409545424, -4.409545424}
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