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Simplifying x(13 + -1x) + 5x = -2 (13 * x + -1x * x) + 5x = -2 (13x + -1x2) + 5x = -2 Reorder the terms: 13x + 5x + -1x2 = -2 Combine like terms: 13x + 5x = 18x 18x + -1x2 = -2 Solving 18x + -1x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 18x + -1x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -18x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -18x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -18x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -18x + x2 = 0 + 2 -18x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -18x + x2 = 2 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 2 + 81 Reorder the terms: 81 + -18x + x2 = 2 + 81 Combine like terms: 2 + 81 = 83 81 + -18x + x2 = 83 Factor a perfect square on the left side: (x + -9)(x + -9) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + -9) equal to 9.110433579 and -9.110433579.Subproblem 1
x + -9 = 9.110433579 Simplifying x + -9 = 9.110433579 Reorder the terms: -9 + x = 9.110433579 Solving -9 + x = 9.110433579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.110433579 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.110433579 + 9 x = 9.110433579 + 9 Combine like terms: 9.110433579 + 9 = 18.110433579 x = 18.110433579 Simplifying x = 18.110433579Subproblem 2
x + -9 = -9.110433579 Simplifying x + -9 = -9.110433579 Reorder the terms: -9 + x = -9.110433579 Solving -9 + x = -9.110433579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.110433579 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.110433579 + 9 x = -9.110433579 + 9 Combine like terms: -9.110433579 + 9 = -0.110433579 x = -0.110433579 Simplifying x = -0.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.110433579, -0.110433579}
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