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Simplifying 9x2 + -2x + 25 = 8x2 + 81 Reorder the terms: 25 + -2x + 9x2 = 8x2 + 81 Reorder the terms: 25 + -2x + 9x2 = 81 + 8x2 Solving 25 + -2x + 9x2 = 81 + 8x2 Solving for variable 'x'. Reorder the terms: 25 + -81 + -2x + 9x2 + -8x2 = 81 + 8x2 + -81 + -8x2 Combine like terms: 25 + -81 = -56 -56 + -2x + 9x2 + -8x2 = 81 + 8x2 + -81 + -8x2 Combine like terms: 9x2 + -8x2 = 1x2 -56 + -2x + 1x2 = 81 + 8x2 + -81 + -8x2 Reorder the terms: -56 + -2x + 1x2 = 81 + -81 + 8x2 + -8x2 Combine like terms: 81 + -81 = 0 -56 + -2x + 1x2 = 0 + 8x2 + -8x2 -56 + -2x + 1x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -56 + -2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -2x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -2x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -2x + x2 = 0 + 56 -2x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -2x + x2 = 56 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 = 56 + 1 Reorder the terms: 1 + -2x + x2 = 56 + 1 Combine like terms: 56 + 1 = 57 1 + -2x + x2 = 57 Factor a perfect square on the left side: (x + -1)(x + -1) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -1) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -1 = 7.549834435 Simplifying x + -1 = 7.549834435 Reorder the terms: -1 + x = 7.549834435 Solving -1 + x = 7.549834435 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 = 7.549834435 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.549834435 + 1 x = 7.549834435 + 1 Combine like terms: 7.549834435 + 1 = 8.549834435 x = 8.549834435 Simplifying x = 8.549834435Subproblem 2
x + -1 = -7.549834435 Simplifying x + -1 = -7.549834435 Reorder the terms: -1 + x = -7.549834435 Solving -1 + x = -7.549834435 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 = -7.549834435 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.549834435 + 1 x = -7.549834435 + 1 Combine like terms: -7.549834435 + 1 = -6.549834435 x = -6.549834435 Simplifying x = -6.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.549834435, -6.549834435}
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