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Simplifying 36x2 + -49x + -9 = 0 Reorder the terms: -9 + -49x + 36x2 = 0 Solving -9 + -49x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.25 + -1.361111111x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.361111111x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.361111111x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.361111111x + x2 = 0 + 0.25 -1.361111111x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.361111111x + x2 = 0.25 The x term is -1.361111111x. Take half its coefficient (-0.6805555555). Square it (0.4631558641) and add it to both sides. Add '0.4631558641' to each side of the equation. -1.361111111x + 0.4631558641 + x2 = 0.25 + 0.4631558641 Reorder the terms: 0.4631558641 + -1.361111111x + x2 = 0.25 + 0.4631558641 Combine like terms: 0.25 + 0.4631558641 = 0.7131558641 0.4631558641 + -1.361111111x + x2 = 0.7131558641 Factor a perfect square on the left side: (x + -0.6805555555)(x + -0.6805555555) = 0.7131558641 Calculate the square root of the right side: 0.844485562 Break this problem into two subproblems by setting (x + -0.6805555555) equal to 0.844485562 and -0.844485562.Subproblem 1
x + -0.6805555555 = 0.844485562 Simplifying x + -0.6805555555 = 0.844485562 Reorder the terms: -0.6805555555 + x = 0.844485562 Solving -0.6805555555 + x = 0.844485562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6805555555' to each side of the equation. -0.6805555555 + 0.6805555555 + x = 0.844485562 + 0.6805555555 Combine like terms: -0.6805555555 + 0.6805555555 = 0.0000000000 0.0000000000 + x = 0.844485562 + 0.6805555555 x = 0.844485562 + 0.6805555555 Combine like terms: 0.844485562 + 0.6805555555 = 1.5250411175 x = 1.5250411175 Simplifying x = 1.5250411175Subproblem 2
x + -0.6805555555 = -0.844485562 Simplifying x + -0.6805555555 = -0.844485562 Reorder the terms: -0.6805555555 + x = -0.844485562 Solving -0.6805555555 + x = -0.844485562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6805555555' to each side of the equation. -0.6805555555 + 0.6805555555 + x = -0.844485562 + 0.6805555555 Combine like terms: -0.6805555555 + 0.6805555555 = 0.0000000000 0.0000000000 + x = -0.844485562 + 0.6805555555 x = -0.844485562 + 0.6805555555 Combine like terms: -0.844485562 + 0.6805555555 = -0.1639300065 x = -0.1639300065 Simplifying x = -0.1639300065Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5250411175, -0.1639300065}
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