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Simplifying x2 + -11x + -11 = -1x2 + -13x + 48 Reorder the terms: -11 + -11x + x2 = -1x2 + -13x + 48 Reorder the terms: -11 + -11x + x2 = 48 + -13x + -1x2 Solving -11 + -11x + x2 = 48 + -13x + -1x2 Solving for variable 'x'. Reorder the terms: -11 + -48 + -11x + 13x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2 Combine like terms: -11 + -48 = -59 -59 + -11x + 13x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2 Combine like terms: -11x + 13x = 2x -59 + 2x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2 Combine like terms: x2 + x2 = 2x2 -59 + 2x + 2x2 = 48 + -13x + -1x2 + -48 + 13x + x2 Reorder the terms: -59 + 2x + 2x2 = 48 + -48 + -13x + 13x + -1x2 + x2 Combine like terms: 48 + -48 = 0 -59 + 2x + 2x2 = 0 + -13x + 13x + -1x2 + x2 -59 + 2x + 2x2 = -13x + 13x + -1x2 + x2 Combine like terms: -13x + 13x = 0 -59 + 2x + 2x2 = 0 + -1x2 + x2 -59 + 2x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -59 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -29.5 + x + x2 = 0 Move the constant term to the right: Add '29.5' to each side of the equation. -29.5 + x + 29.5 + x2 = 0 + 29.5 Reorder the terms: -29.5 + 29.5 + x + x2 = 0 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x + x2 = 0 + 29.5 x + x2 = 0 + 29.5 Combine like terms: 0 + 29.5 = 29.5 x + x2 = 29.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 29.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 29.5 + 0.25 Combine like terms: 29.5 + 0.25 = 29.75 1.25 + x2 = 29.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 29.75 Calculate the square root of the right side: 5.454356057 Break this problem into two subproblems by setting (x + 0.5) equal to 5.454356057 and -5.454356057.Subproblem 1
x + 0.5 = 5.454356057 Simplifying x + 0.5 = 5.454356057 Reorder the terms: 0.5 + x = 5.454356057 Solving 0.5 + x = 5.454356057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.454356057 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.454356057 + -0.5 x = 5.454356057 + -0.5 Combine like terms: 5.454356057 + -0.5 = 4.954356057 x = 4.954356057 Simplifying x = 4.954356057Subproblem 2
x + 0.5 = -5.454356057 Simplifying x + 0.5 = -5.454356057 Reorder the terms: 0.5 + x = -5.454356057 Solving 0.5 + x = -5.454356057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.454356057 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.454356057 + -0.5 x = -5.454356057 + -0.5 Combine like terms: -5.454356057 + -0.5 = -5.954356057 x = -5.954356057 Simplifying x = -5.954356057Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.954356057, -5.954356057}
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