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Simplifying 2x2 + -1x = 11 Reorder the terms: -1x + 2x2 = 11 Solving -1x + 2x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -1x + 2x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -0.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -0.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -0.5x + x2 = 0 + 5.5 -0.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -0.5x + x2 = 5.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 5.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 5.5 + 0.0625 Combine like terms: 5.5 + 0.0625 = 5.5625 0.0625 + -0.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -0.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -0.25 = 2.358495283 Simplifying x + -0.25 = 2.358495283 Reorder the terms: -0.25 + x = 2.358495283 Solving -0.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.358495283 + 0.25 x = 2.358495283 + 0.25 Combine like terms: 2.358495283 + 0.25 = 2.608495283 x = 2.608495283 Simplifying x = 2.608495283Subproblem 2
x + -0.25 = -2.358495283 Simplifying x + -0.25 = -2.358495283 Reorder the terms: -0.25 + x = -2.358495283 Solving -0.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.358495283 + 0.25 x = -2.358495283 + 0.25 Combine like terms: -2.358495283 + 0.25 = -2.108495283 x = -2.108495283 Simplifying x = -2.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.608495283, -2.108495283}
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