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Simplifying x(11x + -7) = 13x + 25 Reorder the terms: x(-7 + 11x) = 13x + 25 (-7 * x + 11x * x) = 13x + 25 (-7x + 11x2) = 13x + 25 Reorder the terms: -7x + 11x2 = 25 + 13x Solving -7x + 11x2 = 25 + 13x Solving for variable 'x'. Reorder the terms: -25 + -7x + -13x + 11x2 = 25 + 13x + -25 + -13x Combine like terms: -7x + -13x = -20x -25 + -20x + 11x2 = 25 + 13x + -25 + -13x Reorder the terms: -25 + -20x + 11x2 = 25 + -25 + 13x + -13x Combine like terms: 25 + -25 = 0 -25 + -20x + 11x2 = 0 + 13x + -13x -25 + -20x + 11x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -25 + -20x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.272727273 + -1.818181818x + x2 = 0 Move the constant term to the right: Add '2.272727273' to each side of the equation. -2.272727273 + -1.818181818x + 2.272727273 + x2 = 0 + 2.272727273 Reorder the terms: -2.272727273 + 2.272727273 + -1.818181818x + x2 = 0 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + -1.818181818x + x2 = 0 + 2.272727273 -1.818181818x + x2 = 0 + 2.272727273 Combine like terms: 0 + 2.272727273 = 2.272727273 -1.818181818x + x2 = 2.272727273 The x term is -1.818181818x. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818x + 0.8264462808 + x2 = 2.272727273 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818x + x2 = 2.272727273 + 0.8264462808 Combine like terms: 2.272727273 + 0.8264462808 = 3.0991735538 0.8264462808 + -1.818181818x + x2 = 3.0991735538 Factor a perfect square on the left side: (x + -0.909090909)(x + -0.909090909) = 3.0991735538 Calculate the square root of the right side: 1.760446976 Break this problem into two subproblems by setting (x + -0.909090909) equal to 1.760446976 and -1.760446976.Subproblem 1
x + -0.909090909 = 1.760446976 Simplifying x + -0.909090909 = 1.760446976 Reorder the terms: -0.909090909 + x = 1.760446976 Solving -0.909090909 + x = 1.760446976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = 1.760446976 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = 1.760446976 + 0.909090909 x = 1.760446976 + 0.909090909 Combine like terms: 1.760446976 + 0.909090909 = 2.669537885 x = 2.669537885 Simplifying x = 2.669537885Subproblem 2
x + -0.909090909 = -1.760446976 Simplifying x + -0.909090909 = -1.760446976 Reorder the terms: -0.909090909 + x = -1.760446976 Solving -0.909090909 + x = -1.760446976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = -1.760446976 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = -1.760446976 + 0.909090909 x = -1.760446976 + 0.909090909 Combine like terms: -1.760446976 + 0.909090909 = -0.851356067 x = -0.851356067 Simplifying x = -0.851356067Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.669537885, -0.851356067}
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