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Simplifying 3x2 + -2x + -11 = x2 + -5x Reorder the terms: -11 + -2x + 3x2 = x2 + -5x Reorder the terms: -11 + -2x + 3x2 = -5x + x2 Solving -11 + -2x + 3x2 = -5x + x2 Solving for variable 'x'. Reorder the terms: -11 + -2x + 5x + 3x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: -2x + 5x = 3x -11 + 3x + 3x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -11 + 3x + 2x2 = -5x + x2 + 5x + -1x2 Reorder the terms: -11 + 3x + 2x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -11 + 3x + 2x2 = 0 + x2 + -1x2 -11 + 3x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 1.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 1.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 1.5x + x2 = 0 + 5.5 1.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 1.5x + x2 = 5.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.5 + 0.5625 Combine like terms: 5.5 + 0.5625 = 6.0625 0.5625 + 1.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 0.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 0.75 = 2.46221445 Simplifying x + 0.75 = 2.46221445 Reorder the terms: 0.75 + x = 2.46221445 Solving 0.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.46221445 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.46221445 + -0.75 x = 2.46221445 + -0.75 Combine like terms: 2.46221445 + -0.75 = 1.71221445 x = 1.71221445 Simplifying x = 1.71221445Subproblem 2
x + 0.75 = -2.46221445 Simplifying x + 0.75 = -2.46221445 Reorder the terms: 0.75 + x = -2.46221445 Solving 0.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.46221445 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.46221445 + -0.75 x = -2.46221445 + -0.75 Combine like terms: -2.46221445 + -0.75 = -3.21221445 x = -3.21221445 Simplifying x = -3.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.71221445, -3.21221445}
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