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Simplifying 8x + -11x(x + -2) = -8 Reorder the terms: 8x + -11x(-2 + x) = -8 8x + (-2 * -11x + x * -11x) = -8 8x + (22x + -11x2) = -8 Combine like terms: 8x + 22x = 30x 30x + -11x2 = -8 Solving 30x + -11x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + 30x + -11x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 30x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.7272727273 + -2.727272727x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -2.727272727x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -2.727272727x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -2.727272727x + x2 = 0 + 0.7272727273 -2.727272727x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -2.727272727x + x2 = 0.7272727273 The x term is -2.727272727x. Take half its coefficient (-1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. -2.727272727x + 1.859504133 + x2 = 0.7272727273 + 1.859504133 Reorder the terms: 1.859504133 + -2.727272727x + x2 = 0.7272727273 + 1.859504133 Combine like terms: 0.7272727273 + 1.859504133 = 2.5867768603 1.859504133 + -2.727272727x + x2 = 2.5867768603 Factor a perfect square on the left side: (x + -1.363636364)(x + -1.363636364) = 2.5867768603 Calculate the square root of the right side: 1.608346001 Break this problem into two subproblems by setting (x + -1.363636364) equal to 1.608346001 and -1.608346001.Subproblem 1
x + -1.363636364 = 1.608346001 Simplifying x + -1.363636364 = 1.608346001 Reorder the terms: -1.363636364 + x = 1.608346001 Solving -1.363636364 + x = 1.608346001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = 1.608346001 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = 1.608346001 + 1.363636364 x = 1.608346001 + 1.363636364 Combine like terms: 1.608346001 + 1.363636364 = 2.971982365 x = 2.971982365 Simplifying x = 2.971982365Subproblem 2
x + -1.363636364 = -1.608346001 Simplifying x + -1.363636364 = -1.608346001 Reorder the terms: -1.363636364 + x = -1.608346001 Solving -1.363636364 + x = -1.608346001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = -1.608346001 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = -1.608346001 + 1.363636364 x = -1.608346001 + 1.363636364 Combine like terms: -1.608346001 + 1.363636364 = -0.244709637 x = -0.244709637 Simplifying x = -0.244709637Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.971982365, -0.244709637}
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