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Simplifying 2x2 + -1x + -1 = 105 Reorder the terms: -1 + -1x + 2x2 = 105 Solving -1 + -1x + 2x2 = 105 Solving for variable 'x'. Reorder the terms: -1 + -105 + -1x + 2x2 = 105 + -105 Combine like terms: -1 + -105 = -106 -106 + -1x + 2x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -106 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -53 + -0.5x + x2 = 0 Move the constant term to the right: Add '53' to each side of the equation. -53 + -0.5x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -0.5x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -0.5x + x2 = 0 + 53 -0.5x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -0.5x + x2 = 53 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 = 53 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 53 + 0.0625 Combine like terms: 53 + 0.0625 = 53.0625 0.0625 + -0.5x + x2 = 53.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 53.0625 Calculate the square root of the right side: 7.284401142 Break this problem into two subproblems by setting (x + -0.25) equal to 7.284401142 and -7.284401142.Subproblem 1
x + -0.25 = 7.284401142 Simplifying x + -0.25 = 7.284401142 Reorder the terms: -0.25 + x = 7.284401142 Solving -0.25 + x = 7.284401142 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 = 7.284401142 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 7.284401142 + 0.25 x = 7.284401142 + 0.25 Combine like terms: 7.284401142 + 0.25 = 7.534401142 x = 7.534401142 Simplifying x = 7.534401142Subproblem 2
x + -0.25 = -7.284401142 Simplifying x + -0.25 = -7.284401142 Reorder the terms: -0.25 + x = -7.284401142 Solving -0.25 + x = -7.284401142 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 = -7.284401142 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -7.284401142 + 0.25 x = -7.284401142 + 0.25 Combine like terms: -7.284401142 + 0.25 = -7.034401142 x = -7.034401142 Simplifying x = -7.034401142Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.534401142, -7.034401142}
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