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Simplifying 0 = x2 + 5x + -183 Reorder the terms: 0 = -183 + 5x + x2 Solving 0 = -183 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 183 = 183 183 + -5x + -1x2 = -183 + 5x + x2 + 183 + -5x + -1x2 Reorder the terms: 183 + -5x + -1x2 = -183 + 183 + 5x + -5x + x2 + -1x2 Combine like terms: -183 + 183 = 0 183 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 183 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 183 + -5x + -1x2 = 0 + x2 + -1x2 183 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 183 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -183 + 5x + x2 = 0 Move the constant term to the right: Add '183' to each side of the equation. -183 + 5x + 183 + x2 = 0 + 183 Reorder the terms: -183 + 183 + 5x + x2 = 0 + 183 Combine like terms: -183 + 183 = 0 0 + 5x + x2 = 0 + 183 5x + x2 = 0 + 183 Combine like terms: 0 + 183 = 183 5x + x2 = 183 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 183 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 183 + 6.25 Combine like terms: 183 + 6.25 = 189.25 6.25 + 5x + x2 = 189.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 189.25 Calculate the square root of the right side: 13.756816492 Break this problem into two subproblems by setting (x + 2.5) equal to 13.756816492 and -13.756816492.Subproblem 1
x + 2.5 = 13.756816492 Simplifying x + 2.5 = 13.756816492 Reorder the terms: 2.5 + x = 13.756816492 Solving 2.5 + x = 13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.756816492 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.756816492 + -2.5 x = 13.756816492 + -2.5 Combine like terms: 13.756816492 + -2.5 = 11.256816492 x = 11.256816492 Simplifying x = 11.256816492Subproblem 2
x + 2.5 = -13.756816492 Simplifying x + 2.5 = -13.756816492 Reorder the terms: 2.5 + x = -13.756816492 Solving 2.5 + x = -13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.756816492 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.756816492 + -2.5 x = -13.756816492 + -2.5 Combine like terms: -13.756816492 + -2.5 = -16.256816492 x = -16.256816492 Simplifying x = -16.256816492Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.256816492, -16.256816492}
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