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Simplifying 9x2 + -62x + -108 = 0 Reorder the terms: -108 + -62x + 9x2 = 0 Solving -108 + -62x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12 + -6.888888889x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -6.888888889x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -6.888888889x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6.888888889x + x2 = 0 + 12 -6.888888889x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6.888888889x + x2 = 12 The x term is -6.888888889x. Take half its coefficient (-3.444444445). Square it (11.86419753) and add it to both sides. Add '11.86419753' to each side of the equation. -6.888888889x + 11.86419753 + x2 = 12 + 11.86419753 Reorder the terms: 11.86419753 + -6.888888889x + x2 = 12 + 11.86419753 Combine like terms: 12 + 11.86419753 = 23.86419753 11.86419753 + -6.888888889x + x2 = 23.86419753 Factor a perfect square on the left side: (x + -3.444444445)(x + -3.444444445) = 23.86419753 Calculate the square root of the right side: 4.885099541 Break this problem into two subproblems by setting (x + -3.444444445) equal to 4.885099541 and -4.885099541.Subproblem 1
x + -3.444444445 = 4.885099541 Simplifying x + -3.444444445 = 4.885099541 Reorder the terms: -3.444444445 + x = 4.885099541 Solving -3.444444445 + x = 4.885099541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.444444445' to each side of the equation. -3.444444445 + 3.444444445 + x = 4.885099541 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = 4.885099541 + 3.444444445 x = 4.885099541 + 3.444444445 Combine like terms: 4.885099541 + 3.444444445 = 8.329543986 x = 8.329543986 Simplifying x = 8.329543986Subproblem 2
x + -3.444444445 = -4.885099541 Simplifying x + -3.444444445 = -4.885099541 Reorder the terms: -3.444444445 + x = -4.885099541 Solving -3.444444445 + x = -4.885099541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.444444445' to each side of the equation. -3.444444445 + 3.444444445 + x = -4.885099541 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = -4.885099541 + 3.444444445 x = -4.885099541 + 3.444444445 Combine like terms: -4.885099541 + 3.444444445 = -1.440655096 x = -1.440655096 Simplifying x = -1.440655096Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.329543986, -1.440655096}
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