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Simplifying 53x2 + 1 = 49x Reorder the terms: 1 + 53x2 = 49x Solving 1 + 53x2 = 49x Solving for variable 'x'. Reorder the terms: 1 + -49x + 53x2 = 49x + -49x Combine like terms: 49x + -49x = 0 1 + -49x + 53x2 = 0 Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. 0.01886792453 + -0.9245283019x + x2 = 0 Move the constant term to the right: Add '-0.01886792453' to each side of the equation. 0.01886792453 + -0.9245283019x + -0.01886792453 + x2 = 0 + -0.01886792453 Reorder the terms: 0.01886792453 + -0.01886792453 + -0.9245283019x + x2 = 0 + -0.01886792453 Combine like terms: 0.01886792453 + -0.01886792453 = 0.00000000000 0.00000000000 + -0.9245283019x + x2 = 0 + -0.01886792453 -0.9245283019x + x2 = 0 + -0.01886792453 Combine like terms: 0 + -0.01886792453 = -0.01886792453 -0.9245283019x + x2 = -0.01886792453 The x term is -0.9245283019x. Take half its coefficient (-0.462264151). Square it (0.2136881453) and add it to both sides. Add '0.2136881453' to each side of the equation. -0.9245283019x + 0.2136881453 + x2 = -0.01886792453 + 0.2136881453 Reorder the terms: 0.2136881453 + -0.9245283019x + x2 = -0.01886792453 + 0.2136881453 Combine like terms: -0.01886792453 + 0.2136881453 = 0.19482022077 0.2136881453 + -0.9245283019x + x2 = 0.19482022077 Factor a perfect square on the left side: (x + -0.462264151)(x + -0.462264151) = 0.19482022077 Calculate the square root of the right side: 0.441384436 Break this problem into two subproblems by setting (x + -0.462264151) equal to 0.441384436 and -0.441384436.Subproblem 1
x + -0.462264151 = 0.441384436 Simplifying x + -0.462264151 = 0.441384436 Reorder the terms: -0.462264151 + x = 0.441384436 Solving -0.462264151 + x = 0.441384436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.462264151' to each side of the equation. -0.462264151 + 0.462264151 + x = 0.441384436 + 0.462264151 Combine like terms: -0.462264151 + 0.462264151 = 0.000000000 0.000000000 + x = 0.441384436 + 0.462264151 x = 0.441384436 + 0.462264151 Combine like terms: 0.441384436 + 0.462264151 = 0.903648587 x = 0.903648587 Simplifying x = 0.903648587Subproblem 2
x + -0.462264151 = -0.441384436 Simplifying x + -0.462264151 = -0.441384436 Reorder the terms: -0.462264151 + x = -0.441384436 Solving -0.462264151 + x = -0.441384436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.462264151' to each side of the equation. -0.462264151 + 0.462264151 + x = -0.441384436 + 0.462264151 Combine like terms: -0.462264151 + 0.462264151 = 0.000000000 0.000000000 + x = -0.441384436 + 0.462264151 x = -0.441384436 + 0.462264151 Combine like terms: -0.441384436 + 0.462264151 = 0.020879715 x = 0.020879715 Simplifying x = 0.020879715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.903648587, 0.020879715}
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