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Simplifying 2x2 + -1x2 + -5x + -5 = 11 Reorder the terms: -5 + -5x + 2x2 + -1x2 = 11 Combine like terms: 2x2 + -1x2 = 1x2 -5 + -5x + 1x2 = 11 Solving -5 + -5x + 1x2 = 11 Solving for variable 'x'. Reorder the terms: -5 + -11 + -5x + 1x2 = 11 + -11 Combine like terms: -5 + -11 = -16 -16 + -5x + 1x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -16 + -5x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5x + x2 = 0 + 16 -5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5x + x2 = 16 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 = 16 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + -5x + x2 = 22.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -2.5 = 4.716990566 Simplifying x + -2.5 = 4.716990566 Reorder the terms: -2.5 + x = 4.716990566 Solving -2.5 + x = 4.716990566 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 = 4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.716990566 + 2.5 x = 4.716990566 + 2.5 Combine like terms: 4.716990566 + 2.5 = 7.216990566 x = 7.216990566 Simplifying x = 7.216990566Subproblem 2
x + -2.5 = -4.716990566 Simplifying x + -2.5 = -4.716990566 Reorder the terms: -2.5 + x = -4.716990566 Solving -2.5 + x = -4.716990566 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 = -4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.716990566 + 2.5 x = -4.716990566 + 2.5 Combine like terms: -4.716990566 + 2.5 = -2.216990566 x = -2.216990566 Simplifying x = -2.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.216990566, -2.216990566}
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