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Simplifying 18x2 + 18x + -317 = 0 Reorder the terms: -317 + 18x + 18x2 = 0 Solving -317 + 18x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -17.61111111 + x + x2 = 0 Move the constant term to the right: Add '17.61111111' to each side of the equation. -17.61111111 + x + 17.61111111 + x2 = 0 + 17.61111111 Reorder the terms: -17.61111111 + 17.61111111 + x + x2 = 0 + 17.61111111 Combine like terms: -17.61111111 + 17.61111111 = 0.00000000 0.00000000 + x + x2 = 0 + 17.61111111 x + x2 = 0 + 17.61111111 Combine like terms: 0 + 17.61111111 = 17.61111111 x + x2 = 17.61111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 17.61111111 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 17.61111111 + 0.25 Combine like terms: 17.61111111 + 0.25 = 17.86111111 1.25 + x2 = 17.86111111 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17.86111111 Calculate the square root of the right side: 4.226240778 Break this problem into two subproblems by setting (x + 0.5) equal to 4.226240778 and -4.226240778.Subproblem 1
x + 0.5 = 4.226240778 Simplifying x + 0.5 = 4.226240778 Reorder the terms: 0.5 + x = 4.226240778 Solving 0.5 + x = 4.226240778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.226240778 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.226240778 + -0.5 x = 4.226240778 + -0.5 Combine like terms: 4.226240778 + -0.5 = 3.726240778 x = 3.726240778 Simplifying x = 3.726240778Subproblem 2
x + 0.5 = -4.226240778 Simplifying x + 0.5 = -4.226240778 Reorder the terms: 0.5 + x = -4.226240778 Solving 0.5 + x = -4.226240778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.226240778 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.226240778 + -0.5 x = -4.226240778 + -0.5 Combine like terms: -4.226240778 + -0.5 = -4.726240778 x = -4.726240778 Simplifying x = -4.726240778Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.726240778, -4.726240778}
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