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Simplifying (11.050000) + -1(11.050000x) + -2x2 = 0 11.050000 + -1(11.050000x) + -2x2 = 0 Remove parenthesis around (11.050000x) 11.050000 + -1 * 11.050000x + -2x2 = 0 Multiply -1 * 11.050000 11.050000 + -11.05x + -2x2 = 0 Solving 11.050000 + -11.05x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.525 + 5.525x + x2 = 0 Move the constant term to the right: Add '5.525' to each side of the equation. -5.525 + 5.525x + 5.525 + x2 = 0 + 5.525 Reorder the terms: -5.525 + 5.525 + 5.525x + x2 = 0 + 5.525 Combine like terms: -5.525 + 5.525 = 0.000 0.000 + 5.525x + x2 = 0 + 5.525 5.525x + x2 = 0 + 5.525 Combine like terms: 0 + 5.525 = 5.525 5.525x + x2 = 5.525 The x term is 5.525x. Take half its coefficient (2.7625). Square it (7.63140625) and add it to both sides. Add '7.63140625' to each side of the equation. 5.525x + 7.63140625 + x2 = 5.525 + 7.63140625 Reorder the terms: 7.63140625 + 5.525x + x2 = 5.525 + 7.63140625 Combine like terms: 5.525 + 7.63140625 = 13.15640625 7.63140625 + 5.525x + x2 = 13.15640625 Factor a perfect square on the left side: (x + 2.7625)(x + 2.7625) = 13.15640625 Calculate the square root of the right side: 3.627176071 Break this problem into two subproblems by setting (x + 2.7625) equal to 3.627176071 and -3.627176071.Subproblem 1
x + 2.7625 = 3.627176071 Simplifying x + 2.7625 = 3.627176071 Reorder the terms: 2.7625 + x = 3.627176071 Solving 2.7625 + x = 3.627176071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7625' to each side of the equation. 2.7625 + -2.7625 + x = 3.627176071 + -2.7625 Combine like terms: 2.7625 + -2.7625 = 0.0000 0.0000 + x = 3.627176071 + -2.7625 x = 3.627176071 + -2.7625 Combine like terms: 3.627176071 + -2.7625 = 0.864676071 x = 0.864676071 Simplifying x = 0.864676071Subproblem 2
x + 2.7625 = -3.627176071 Simplifying x + 2.7625 = -3.627176071 Reorder the terms: 2.7625 + x = -3.627176071 Solving 2.7625 + x = -3.627176071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7625' to each side of the equation. 2.7625 + -2.7625 + x = -3.627176071 + -2.7625 Combine like terms: 2.7625 + -2.7625 = 0.0000 0.0000 + x = -3.627176071 + -2.7625 x = -3.627176071 + -2.7625 Combine like terms: -3.627176071 + -2.7625 = -6.389676071 x = -6.389676071 Simplifying x = -6.389676071Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.864676071, -6.389676071}
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