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Simplifying 0 = 2x2 + 11x + -25 Reorder the terms: 0 = -25 + 11x + 2x2 Solving 0 = -25 + 11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -11x + -2x2 = -25 + 11x + 2x2 + 25 + -11x + -2x2 Reorder the terms: 25 + -11x + -2x2 = -25 + 25 + 11x + -11x + 2x2 + -2x2 Combine like terms: -25 + 25 = 0 25 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2 25 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 25 + -11x + -2x2 = 0 + 2x2 + -2x2 25 + -11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 25 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 5.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 5.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 5.5x + x2 = 0 + 12.5 5.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 5.5x + x2 = 12.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 12.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 12.5 + 7.5625 Combine like terms: 12.5 + 7.5625 = 20.0625 7.5625 + 5.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 2.75) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 2.75 = 4.479118217 Simplifying x + 2.75 = 4.479118217 Reorder the terms: 2.75 + x = 4.479118217 Solving 2.75 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.479118217 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.479118217 + -2.75 x = 4.479118217 + -2.75 Combine like terms: 4.479118217 + -2.75 = 1.729118217 x = 1.729118217 Simplifying x = 1.729118217Subproblem 2
x + 2.75 = -4.479118217 Simplifying x + 2.75 = -4.479118217 Reorder the terms: 2.75 + x = -4.479118217 Solving 2.75 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.479118217 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.479118217 + -2.75 x = -4.479118217 + -2.75 Combine like terms: -4.479118217 + -2.75 = -7.229118217 x = -7.229118217 Simplifying x = -7.229118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.729118217, -7.229118217}
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