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Simplifying 25 = 11x + x2 Solving 25 = 11x + x2 Solving for variable 'x'. Reorder the terms: 25 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 25 + -11x + -1x2 = 0 + x2 + -1x2 25 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 11x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 11x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 11x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 11x + x2 = 0 + 25 11x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 11x + x2 = 25 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 = 25 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 25 + 30.25 Combine like terms: 25 + 30.25 = 55.25 30.25 + 11x + x2 = 55.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 5.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 5.5 = 7.433034374 Simplifying x + 5.5 = 7.433034374 Reorder the terms: 5.5 + x = 7.433034374 Solving 5.5 + x = 7.433034374 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 = 7.433034374 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.433034374 + -5.5 x = 7.433034374 + -5.5 Combine like terms: 7.433034374 + -5.5 = 1.933034374 x = 1.933034374 Simplifying x = 1.933034374Subproblem 2
x + 5.5 = -7.433034374 Simplifying x + 5.5 = -7.433034374 Reorder the terms: 5.5 + x = -7.433034374 Solving 5.5 + x = -7.433034374 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 = -7.433034374 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.433034374 + -5.5 x = -7.433034374 + -5.5 Combine like terms: -7.433034374 + -5.5 = -12.933034374 x = -12.933034374 Simplifying x = -12.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.933034374, -12.933034374}
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