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Simplifying 36x2 + -49x + 4 = 0 Reorder the terms: 4 + -49x + 36x2 = 0 Solving 4 + -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'. 0.1111111111 + -1.361111111x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -1.361111111x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -1.361111111x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -1.361111111x + x2 = 0 + -0.1111111111 -1.361111111x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -1.361111111x + x2 = -0.1111111111 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 = -0.1111111111 + 0.4631558641 Reorder the terms: 0.4631558641 + -1.361111111x + x2 = -0.1111111111 + 0.4631558641 Combine like terms: -0.1111111111 + 0.4631558641 = 0.352044753 0.4631558641 + -1.361111111x + x2 = 0.352044753 Factor a perfect square on the left side: (x + -0.6805555555)(x + -0.6805555555) = 0.352044753 Calculate the square root of the right side: 0.593333593 Break this problem into two subproblems by setting (x + -0.6805555555) equal to 0.593333593 and -0.593333593.Subproblem 1
x + -0.6805555555 = 0.593333593 Simplifying x + -0.6805555555 = 0.593333593 Reorder the terms: -0.6805555555 + x = 0.593333593 Solving -0.6805555555 + x = 0.593333593 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 = 0.593333593 + 0.6805555555 Combine like terms: -0.6805555555 + 0.6805555555 = 0.0000000000 0.0000000000 + x = 0.593333593 + 0.6805555555 x = 0.593333593 + 0.6805555555 Combine like terms: 0.593333593 + 0.6805555555 = 1.2738891485 x = 1.2738891485 Simplifying x = 1.2738891485Subproblem 2
x + -0.6805555555 = -0.593333593 Simplifying x + -0.6805555555 = -0.593333593 Reorder the terms: -0.6805555555 + x = -0.593333593 Solving -0.6805555555 + x = -0.593333593 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 = -0.593333593 + 0.6805555555 Combine like terms: -0.6805555555 + 0.6805555555 = 0.0000000000 0.0000000000 + x = -0.593333593 + 0.6805555555 x = -0.593333593 + 0.6805555555 Combine like terms: -0.593333593 + 0.6805555555 = 0.0872219625 x = 0.0872219625 Simplifying x = 0.0872219625Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2738891485, 0.0872219625}
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