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Simplifying x(9 + -1x) + 9x = -6 (9 * x + -1x * x) + 9x = -6 (9x + -1x2) + 9x = -6 Reorder the terms: 9x + 9x + -1x2 = -6 Combine like terms: 9x + 9x = 18x 18x + -1x2 = -6 Solving 18x + -1x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 18x + -1x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -18x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -18x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -18x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -18x + x2 = 0 + 6 -18x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -18x + x2 = 6 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 = 6 + 81 Reorder the terms: 81 + -18x + x2 = 6 + 81 Combine like terms: 6 + 81 = 87 81 + -18x + x2 = 87 Factor a perfect square on the left side: (x + -9)(x + -9) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + -9) equal to 9.327379053 and -9.327379053.Subproblem 1
x + -9 = 9.327379053 Simplifying x + -9 = 9.327379053 Reorder the terms: -9 + x = 9.327379053 Solving -9 + x = 9.327379053 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 = 9.327379053 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.327379053 + 9 x = 9.327379053 + 9 Combine like terms: 9.327379053 + 9 = 18.327379053 x = 18.327379053 Simplifying x = 18.327379053Subproblem 2
x + -9 = -9.327379053 Simplifying x + -9 = -9.327379053 Reorder the terms: -9 + x = -9.327379053 Solving -9 + x = -9.327379053 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 = -9.327379053 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.327379053 + 9 x = -9.327379053 + 9 Combine like terms: -9.327379053 + 9 = -0.327379053 x = -0.327379053 Simplifying x = -0.327379053Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.327379053, -0.327379053}
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