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Simplifying -0.03x2 + 3.7x + -49 = 0 Reorder the terms: -49 + 3.7x + -0.03x2 = 0 Solving -49 + 3.7x + -0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 1633.333333 + -123.3333333x + x2 = 0 Move the constant term to the right: Add '-1633.333333' to each side of the equation. 1633.333333 + -123.3333333x + -1633.333333 + x2 = 0 + -1633.333333 Reorder the terms: 1633.333333 + -1633.333333 + -123.3333333x + x2 = 0 + -1633.333333 Combine like terms: 1633.333333 + -1633.333333 = 0.000000 0.000000 + -123.3333333x + x2 = 0 + -1633.333333 -123.3333333x + x2 = 0 + -1633.333333 Combine like terms: 0 + -1633.333333 = -1633.333333 -123.3333333x + x2 = -1633.333333 The x term is -123.3333333x. Take half its coefficient (-61.66666665). Square it (3802.777776) and add it to both sides. Add '3802.777776' to each side of the equation. -123.3333333x + 3802.777776 + x2 = -1633.333333 + 3802.777776 Reorder the terms: 3802.777776 + -123.3333333x + x2 = -1633.333333 + 3802.777776 Combine like terms: -1633.333333 + 3802.777776 = 2169.444443 3802.777776 + -123.3333333x + x2 = 2169.444443 Factor a perfect square on the left side: (x + -61.66666665)(x + -61.66666665) = 2169.444443 Calculate the square root of the right side: 46.577295359 Break this problem into two subproblems by setting (x + -61.66666665) equal to 46.577295359 and -46.577295359.Subproblem 1
x + -61.66666665 = 46.577295359 Simplifying x + -61.66666665 = 46.577295359 Reorder the terms: -61.66666665 + x = 46.577295359 Solving -61.66666665 + x = 46.577295359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.66666665' to each side of the equation. -61.66666665 + 61.66666665 + x = 46.577295359 + 61.66666665 Combine like terms: -61.66666665 + 61.66666665 = 0.00000000 0.00000000 + x = 46.577295359 + 61.66666665 x = 46.577295359 + 61.66666665 Combine like terms: 46.577295359 + 61.66666665 = 108.243962009 x = 108.243962009 Simplifying x = 108.243962009Subproblem 2
x + -61.66666665 = -46.577295359 Simplifying x + -61.66666665 = -46.577295359 Reorder the terms: -61.66666665 + x = -46.577295359 Solving -61.66666665 + x = -46.577295359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.66666665' to each side of the equation. -61.66666665 + 61.66666665 + x = -46.577295359 + 61.66666665 Combine like terms: -61.66666665 + 61.66666665 = 0.00000000 0.00000000 + x = -46.577295359 + 61.66666665 x = -46.577295359 + 61.66666665 Combine like terms: -46.577295359 + 61.66666665 = 15.089371291 x = 15.089371291 Simplifying x = 15.089371291Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.243962009, 15.089371291}
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