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Simplifying 9x2 + -248x + 540 = 0 Reorder the terms: 540 + -248x + 9x2 = 0 Solving 540 + -248x + 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'. 60 + -27.55555556x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -27.55555556x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -27.55555556x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -27.55555556x + x2 = 0 + -60 -27.55555556x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -27.55555556x + x2 = -60 The x term is -27.55555556x. Take half its coefficient (-13.77777778). Square it (189.8271606) and add it to both sides. Add '189.8271606' to each side of the equation. -27.55555556x + 189.8271606 + x2 = -60 + 189.8271606 Reorder the terms: 189.8271606 + -27.55555556x + x2 = -60 + 189.8271606 Combine like terms: -60 + 189.8271606 = 129.8271606 189.8271606 + -27.55555556x + x2 = 129.8271606 Factor a perfect square on the left side: (x + -13.77777778)(x + -13.77777778) = 129.8271606 Calculate the square root of the right side: 11.394172221 Break this problem into two subproblems by setting (x + -13.77777778) equal to 11.394172221 and -11.394172221.Subproblem 1
x + -13.77777778 = 11.394172221 Simplifying x + -13.77777778 = 11.394172221 Reorder the terms: -13.77777778 + x = 11.394172221 Solving -13.77777778 + x = 11.394172221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.77777778' to each side of the equation. -13.77777778 + 13.77777778 + x = 11.394172221 + 13.77777778 Combine like terms: -13.77777778 + 13.77777778 = 0.00000000 0.00000000 + x = 11.394172221 + 13.77777778 x = 11.394172221 + 13.77777778 Combine like terms: 11.394172221 + 13.77777778 = 25.171950001 x = 25.171950001 Simplifying x = 25.171950001Subproblem 2
x + -13.77777778 = -11.394172221 Simplifying x + -13.77777778 = -11.394172221 Reorder the terms: -13.77777778 + x = -11.394172221 Solving -13.77777778 + x = -11.394172221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.77777778' to each side of the equation. -13.77777778 + 13.77777778 + x = -11.394172221 + 13.77777778 Combine like terms: -13.77777778 + 13.77777778 = 0.00000000 0.00000000 + x = -11.394172221 + 13.77777778 x = -11.394172221 + 13.77777778 Combine like terms: -11.394172221 + 13.77777778 = 2.383605559 x = 2.383605559 Simplifying x = 2.383605559Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.171950001, 2.383605559}
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