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Simplifying (x2 + -2x) = 3x2 + 5x + -11 Reorder the terms: (-2x + x2) = 3x2 + 5x + -11 Remove parenthesis around (-2x + x2) -2x + x2 = 3x2 + 5x + -11 Reorder the terms: -2x + x2 = -11 + 5x + 3x2 Solving -2x + x2 = -11 + 5x + 3x2 Solving for variable 'x'. Reorder the terms: 11 + -2x + -5x + x2 + -3x2 = -11 + 5x + 3x2 + 11 + -5x + -3x2 Combine like terms: -2x + -5x = -7x 11 + -7x + x2 + -3x2 = -11 + 5x + 3x2 + 11 + -5x + -3x2 Combine like terms: x2 + -3x2 = -2x2 11 + -7x + -2x2 = -11 + 5x + 3x2 + 11 + -5x + -3x2 Reorder the terms: 11 + -7x + -2x2 = -11 + 11 + 5x + -5x + 3x2 + -3x2 Combine like terms: -11 + 11 = 0 11 + -7x + -2x2 = 0 + 5x + -5x + 3x2 + -3x2 11 + -7x + -2x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 11 + -7x + -2x2 = 0 + 3x2 + -3x2 11 + -7x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 11 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 3.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 3.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 3.5x + x2 = 0 + 5.5 3.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 3.5x + x2 = 5.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 5.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 5.5 + 3.0625 Combine like terms: 5.5 + 3.0625 = 8.5625 3.0625 + 3.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + 1.75) equal to 2.926174978 and -2.926174978.Subproblem 1
x + 1.75 = 2.926174978 Simplifying x + 1.75 = 2.926174978 Reorder the terms: 1.75 + x = 2.926174978 Solving 1.75 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.926174978 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.926174978 + -1.75 x = 2.926174978 + -1.75 Combine like terms: 2.926174978 + -1.75 = 1.176174978 x = 1.176174978 Simplifying x = 1.176174978Subproblem 2
x + 1.75 = -2.926174978 Simplifying x + 1.75 = -2.926174978 Reorder the terms: 1.75 + x = -2.926174978 Solving 1.75 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.926174978 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.926174978 + -1.75 x = -2.926174978 + -1.75 Combine like terms: -2.926174978 + -1.75 = -4.676174978 x = -4.676174978 Simplifying x = -4.676174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.176174978, -4.676174978}
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