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Simplifying -36x2 + -56x + 36 = 0 Reorder the terms: 36 + -56x + -36x2 = 0 Solving 36 + -56x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -14x + -9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -14x + -9x2)' equal to zero and attempt to solve: Simplifying 9 + -14x + -9x2 = 0 Solving 9 + -14x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.555555556x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.555555556x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.555555556x + x2 = 0 + 1 1.555555556x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.555555556x + x2 = 1 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 1 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 1 + 0.6049382720 Combine like terms: 1 + 0.6049382720 = 1.604938272 0.6049382720 + 1.555555556x + x2 = 1.604938272 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 1.604938272 Calculate the square root of the right side: 1.266861584 Break this problem into two subproblems by setting (x + 0.777777778) equal to 1.266861584 and -1.266861584.Subproblem 1
x + 0.777777778 = 1.266861584 Simplifying x + 0.777777778 = 1.266861584 Reorder the terms: 0.777777778 + x = 1.266861584 Solving 0.777777778 + x = 1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.266861584 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.266861584 + -0.777777778 x = 1.266861584 + -0.777777778 Combine like terms: 1.266861584 + -0.777777778 = 0.489083806 x = 0.489083806 Simplifying x = 0.489083806Subproblem 2
x + 0.777777778 = -1.266861584 Simplifying x + 0.777777778 = -1.266861584 Reorder the terms: 0.777777778 + x = -1.266861584 Solving 0.777777778 + x = -1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.266861584 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.266861584 + -0.777777778 x = -1.266861584 + -0.777777778 Combine like terms: -1.266861584 + -0.777777778 = -2.044639362 x = -2.044639362 Simplifying x = -2.044639362Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.489083806, -2.044639362}Solution
x = {0.489083806, -2.044639362}
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