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Simplifying -36x2 + 70x + -33 = 0 Reorder the terms: -33 + 70x + -36x2 = 0 Solving -33 + 70x + -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'. 0.9166666667 + -1.944444444x + x2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + -1.944444444x + -0.9166666667 + x2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + -1.944444444x + x2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + -1.944444444x + x2 = 0 + -0.9166666667 -1.944444444x + x2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 -1.944444444x + x2 = -0.9166666667 The x term is -1.944444444x. Take half its coefficient (-0.972222222). Square it (0.9452160490) and add it to both sides. Add '0.9452160490' to each side of the equation. -1.944444444x + 0.9452160490 + x2 = -0.9166666667 + 0.9452160490 Reorder the terms: 0.9452160490 + -1.944444444x + x2 = -0.9166666667 + 0.9452160490 Combine like terms: -0.9166666667 + 0.9452160490 = 0.0285493823 0.9452160490 + -1.944444444x + x2 = 0.0285493823 Factor a perfect square on the left side: (x + -0.972222222)(x + -0.972222222) = 0.0285493823 Calculate the square root of the right side: 0.168965625 Break this problem into two subproblems by setting (x + -0.972222222) equal to 0.168965625 and -0.168965625.Subproblem 1
x + -0.972222222 = 0.168965625 Simplifying x + -0.972222222 = 0.168965625 Reorder the terms: -0.972222222 + x = 0.168965625 Solving -0.972222222 + x = 0.168965625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.972222222' to each side of the equation. -0.972222222 + 0.972222222 + x = 0.168965625 + 0.972222222 Combine like terms: -0.972222222 + 0.972222222 = 0.000000000 0.000000000 + x = 0.168965625 + 0.972222222 x = 0.168965625 + 0.972222222 Combine like terms: 0.168965625 + 0.972222222 = 1.141187847 x = 1.141187847 Simplifying x = 1.141187847Subproblem 2
x + -0.972222222 = -0.168965625 Simplifying x + -0.972222222 = -0.168965625 Reorder the terms: -0.972222222 + x = -0.168965625 Solving -0.972222222 + x = -0.168965625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.972222222' to each side of the equation. -0.972222222 + 0.972222222 + x = -0.168965625 + 0.972222222 Combine like terms: -0.972222222 + 0.972222222 = 0.000000000 0.000000000 + x = -0.168965625 + 0.972222222 x = -0.168965625 + 0.972222222 Combine like terms: -0.168965625 + 0.972222222 = 0.803256597 x = 0.803256597 Simplifying x = 0.803256597Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.141187847, 0.803256597}
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