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Simplifying 174 = x2 + 11x Reorder the terms: 174 = 11x + x2 Solving 174 = 11x + x2 Solving for variable 'x'. Reorder the terms: 174 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 174 + -11x + -1x2 = 0 + x2 + -1x2 174 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 174 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -174 + 11x + x2 = 0 Move the constant term to the right: Add '174' to each side of the equation. -174 + 11x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 11x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 11x + x2 = 0 + 174 11x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 11x + x2 = 174 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 174 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 174 + 30.25 Combine like terms: 174 + 30.25 = 204.25 30.25 + 11x + x2 = 204.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (x + 5.5) equal to 14.291605928 and -14.291605928.Subproblem 1
x + 5.5 = 14.291605928 Simplifying x + 5.5 = 14.291605928 Reorder the terms: 5.5 + x = 14.291605928 Solving 5.5 + x = 14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 14.291605928 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 14.291605928 + -5.5 x = 14.291605928 + -5.5 Combine like terms: 14.291605928 + -5.5 = 8.791605928 x = 8.791605928 Simplifying x = 8.791605928Subproblem 2
x + 5.5 = -14.291605928 Simplifying x + 5.5 = -14.291605928 Reorder the terms: 5.5 + x = -14.291605928 Solving 5.5 + x = -14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -14.291605928 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -14.291605928 + -5.5 x = -14.291605928 + -5.5 Combine like terms: -14.291605928 + -5.5 = -19.791605928 x = -19.791605928 Simplifying x = -19.791605928Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.791605928, -19.791605928}
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