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Simplifying 9x2 + -49x + 68 = x Reorder the terms: 68 + -49x + 9x2 = x Solving 68 + -49x + 9x2 = x Solving for variable 'x'. Reorder the terms: 68 + -49x + -1x + 9x2 = x + -1x Combine like terms: -49x + -1x = -50x 68 + -50x + 9x2 = x + -1x Combine like terms: x + -1x = 0 68 + -50x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 7.555555556 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '-7.555555556' to each side of the equation. 7.555555556 + -5.555555556x + -7.555555556 + x2 = 0 + -7.555555556 Reorder the terms: 7.555555556 + -7.555555556 + -5.555555556x + x2 = 0 + -7.555555556 Combine like terms: 7.555555556 + -7.555555556 = 0.000000000 0.000000000 + -5.555555556x + x2 = 0 + -7.555555556 -5.555555556x + x2 = 0 + -7.555555556 Combine like terms: 0 + -7.555555556 = -7.555555556 -5.555555556x + x2 = -7.555555556 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = -7.555555556 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = -7.555555556 + 7.716049384 Combine like terms: -7.555555556 + 7.716049384 = 0.160493828 7.716049384 + -5.555555556x + x2 = 0.160493828 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 0.160493828 Calculate the square root of the right side: 0.400616809 Break this problem into two subproblems by setting (x + -2.777777778) equal to 0.400616809 and -0.400616809.Subproblem 1
x + -2.777777778 = 0.400616809 Simplifying x + -2.777777778 = 0.400616809 Reorder the terms: -2.777777778 + x = 0.400616809 Solving -2.777777778 + x = 0.400616809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 0.400616809 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 0.400616809 + 2.777777778 x = 0.400616809 + 2.777777778 Combine like terms: 0.400616809 + 2.777777778 = 3.178394587 x = 3.178394587 Simplifying x = 3.178394587Subproblem 2
x + -2.777777778 = -0.400616809 Simplifying x + -2.777777778 = -0.400616809 Reorder the terms: -2.777777778 + x = -0.400616809 Solving -2.777777778 + x = -0.400616809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -0.400616809 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -0.400616809 + 2.777777778 x = -0.400616809 + 2.777777778 Combine like terms: -0.400616809 + 2.777777778 = 2.377160969 x = 2.377160969 Simplifying x = 2.377160969Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.178394587, 2.377160969}
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