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Simplifying 4x2 + -91x + 25 = 0 Reorder the terms: 25 + -91x + 4x2 = 0 Solving 25 + -91x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -22.75x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -22.75x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -22.75x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -22.75x + x2 = 0 + -6.25 -22.75x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -22.75x + x2 = -6.25 The x term is -22.75x. Take half its coefficient (-11.375). Square it (129.390625) and add it to both sides. Add '129.390625' to each side of the equation. -22.75x + 129.390625 + x2 = -6.25 + 129.390625 Reorder the terms: 129.390625 + -22.75x + x2 = -6.25 + 129.390625 Combine like terms: -6.25 + 129.390625 = 123.140625 129.390625 + -22.75x + x2 = 123.140625 Factor a perfect square on the left side: (x + -11.375)(x + -11.375) = 123.140625 Calculate the square root of the right side: 11.09687456 Break this problem into two subproblems by setting (x + -11.375) equal to 11.09687456 and -11.09687456.Subproblem 1
x + -11.375 = 11.09687456 Simplifying x + -11.375 = 11.09687456 Reorder the terms: -11.375 + x = 11.09687456 Solving -11.375 + x = 11.09687456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.375' to each side of the equation. -11.375 + 11.375 + x = 11.09687456 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + x = 11.09687456 + 11.375 x = 11.09687456 + 11.375 Combine like terms: 11.09687456 + 11.375 = 22.47187456 x = 22.47187456 Simplifying x = 22.47187456Subproblem 2
x + -11.375 = -11.09687456 Simplifying x + -11.375 = -11.09687456 Reorder the terms: -11.375 + x = -11.09687456 Solving -11.375 + x = -11.09687456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.375' to each side of the equation. -11.375 + 11.375 + x = -11.09687456 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + x = -11.09687456 + 11.375 x = -11.09687456 + 11.375 Combine like terms: -11.09687456 + 11.375 = 0.27812544 x = 0.27812544 Simplifying x = 0.27812544Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.47187456, 0.27812544}
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