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Simplifying 5x2 + -1x = x2 + -9x + 31 Reorder the terms: -1x + 5x2 = x2 + -9x + 31 Reorder the terms: -1x + 5x2 = 31 + -9x + x2 Solving -1x + 5x2 = 31 + -9x + x2 Solving for variable 'x'. Reorder the terms: -31 + -1x + 9x + 5x2 + -1x2 = 31 + -9x + x2 + -31 + 9x + -1x2 Combine like terms: -1x + 9x = 8x -31 + 8x + 5x2 + -1x2 = 31 + -9x + x2 + -31 + 9x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -31 + 8x + 4x2 = 31 + -9x + x2 + -31 + 9x + -1x2 Reorder the terms: -31 + 8x + 4x2 = 31 + -31 + -9x + 9x + x2 + -1x2 Combine like terms: 31 + -31 = 0 -31 + 8x + 4x2 = 0 + -9x + 9x + x2 + -1x2 -31 + 8x + 4x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 -31 + 8x + 4x2 = 0 + x2 + -1x2 -31 + 8x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -31 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.75 + 2x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + 2x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + 2x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + 2x + x2 = 0 + 7.75 2x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 2x + x2 = 7.75 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 = 7.75 + 1 Reorder the terms: 1 + 2x + x2 = 7.75 + 1 Combine like terms: 7.75 + 1 = 8.75 1 + 2x + x2 = 8.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + 1) equal to 2.958039892 and -2.958039892.Subproblem 1
x + 1 = 2.958039892 Simplifying x + 1 = 2.958039892 Reorder the terms: 1 + x = 2.958039892 Solving 1 + x = 2.958039892 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 = 2.958039892 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.958039892 + -1 x = 2.958039892 + -1 Combine like terms: 2.958039892 + -1 = 1.958039892 x = 1.958039892 Simplifying x = 1.958039892Subproblem 2
x + 1 = -2.958039892 Simplifying x + 1 = -2.958039892 Reorder the terms: 1 + x = -2.958039892 Solving 1 + x = -2.958039892 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 = -2.958039892 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.958039892 + -1 x = -2.958039892 + -1 Combine like terms: -2.958039892 + -1 = -3.958039892 x = -3.958039892 Simplifying x = -3.958039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.958039892, -3.958039892}
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