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Simplifying 49x2 = -57x + 60 Reorder the terms: 49x2 = 60 + -57x Solving 49x2 = 60 + -57x Solving for variable 'x'. Reorder the terms: -60 + 57x + 49x2 = 60 + -57x + -60 + 57x Reorder the terms: -60 + 57x + 49x2 = 60 + -60 + -57x + 57x Combine like terms: 60 + -60 = 0 -60 + 57x + 49x2 = 0 + -57x + 57x -60 + 57x + 49x2 = -57x + 57x Combine like terms: -57x + 57x = 0 -60 + 57x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.224489796 + 1.163265306x + x2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + 1.163265306x + 1.224489796 + x2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + 1.163265306x + x2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + 1.163265306x + x2 = 0 + 1.224489796 1.163265306x + x2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 1.163265306x + x2 = 1.224489796 The x term is 1.163265306x. Take half its coefficient (0.581632653). Square it (0.3382965430) and add it to both sides. Add '0.3382965430' to each side of the equation. 1.163265306x + 0.3382965430 + x2 = 1.224489796 + 0.3382965430 Reorder the terms: 0.3382965430 + 1.163265306x + x2 = 1.224489796 + 0.3382965430 Combine like terms: 1.224489796 + 0.3382965430 = 1.562786339 0.3382965430 + 1.163265306x + x2 = 1.562786339 Factor a perfect square on the left side: (x + 0.581632653)(x + 0.581632653) = 1.562786339 Calculate the square root of the right side: 1.25011453 Break this problem into two subproblems by setting (x + 0.581632653) equal to 1.25011453 and -1.25011453.Subproblem 1
x + 0.581632653 = 1.25011453 Simplifying x + 0.581632653 = 1.25011453 Reorder the terms: 0.581632653 + x = 1.25011453 Solving 0.581632653 + x = 1.25011453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.581632653' to each side of the equation. 0.581632653 + -0.581632653 + x = 1.25011453 + -0.581632653 Combine like terms: 0.581632653 + -0.581632653 = 0.000000000 0.000000000 + x = 1.25011453 + -0.581632653 x = 1.25011453 + -0.581632653 Combine like terms: 1.25011453 + -0.581632653 = 0.668481877 x = 0.668481877 Simplifying x = 0.668481877Subproblem 2
x + 0.581632653 = -1.25011453 Simplifying x + 0.581632653 = -1.25011453 Reorder the terms: 0.581632653 + x = -1.25011453 Solving 0.581632653 + x = -1.25011453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.581632653' to each side of the equation. 0.581632653 + -0.581632653 + x = -1.25011453 + -0.581632653 Combine like terms: 0.581632653 + -0.581632653 = 0.000000000 0.000000000 + x = -1.25011453 + -0.581632653 x = -1.25011453 + -0.581632653 Combine like terms: -1.25011453 + -0.581632653 = -1.831747183 x = -1.831747183 Simplifying x = -1.831747183Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.668481877, -1.831747183}
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