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Simplifying 2x(x + 5) + -11 = 4x + 7x + 1 Reorder the terms: 2x(5 + x) + -11 = 4x + 7x + 1 (5 * 2x + x * 2x) + -11 = 4x + 7x + 1 (10x + 2x2) + -11 = 4x + 7x + 1 Reorder the terms: -11 + 10x + 2x2 = 4x + 7x + 1 Reorder the terms: -11 + 10x + 2x2 = 1 + 4x + 7x Combine like terms: 4x + 7x = 11x -11 + 10x + 2x2 = 1 + 11x Solving -11 + 10x + 2x2 = 1 + 11x Solving for variable 'x'. Reorder the terms: -11 + -1 + 10x + -11x + 2x2 = 1 + 11x + -1 + -11x Combine like terms: -11 + -1 = -12 -12 + 10x + -11x + 2x2 = 1 + 11x + -1 + -11x Combine like terms: 10x + -11x = -1x -12 + -1x + 2x2 = 1 + 11x + -1 + -11x Reorder the terms: -12 + -1x + 2x2 = 1 + -1 + 11x + -11x Combine like terms: 1 + -1 = 0 -12 + -1x + 2x2 = 0 + 11x + -11x -12 + -1x + 2x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -12 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -0.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5x + x2 = 0 + 6 -0.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5x + x2 = 6 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 = 6 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 6 + 0.0625 Combine like terms: 6 + 0.0625 = 6.0625 0.0625 + -0.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -0.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -0.25 = 2.46221445 Simplifying x + -0.25 = 2.46221445 Reorder the terms: -0.25 + x = 2.46221445 Solving -0.25 + x = 2.46221445 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 = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.46221445 + 0.25 x = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 x = 2.71221445 Simplifying x = 2.71221445Subproblem 2
x + -0.25 = -2.46221445 Simplifying x + -0.25 = -2.46221445 Reorder the terms: -0.25 + x = -2.46221445 Solving -0.25 + x = -2.46221445 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 = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.46221445 + 0.25 x = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 x = -2.21221445 Simplifying x = -2.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.71221445, -2.21221445}
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