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Simplifying 4x2 + 101x + -65 = 0 Reorder the terms: -65 + 101x + 4x2 = 0 Solving -65 + 101x + 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'. -16.25 + 25.25x + x2 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + 25.25x + 16.25 + x2 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + 25.25x + x2 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + 25.25x + x2 = 0 + 16.25 25.25x + x2 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 25.25x + x2 = 16.25 The x term is 25.25x. Take half its coefficient (12.625). Square it (159.390625) and add it to both sides. Add '159.390625' to each side of the equation. 25.25x + 159.390625 + x2 = 16.25 + 159.390625 Reorder the terms: 159.390625 + 25.25x + x2 = 16.25 + 159.390625 Combine like terms: 16.25 + 159.390625 = 175.640625 159.390625 + 25.25x + x2 = 175.640625 Factor a perfect square on the left side: (x + 12.625)(x + 12.625) = 175.640625 Calculate the square root of the right side: 13.252947785 Break this problem into two subproblems by setting (x + 12.625) equal to 13.252947785 and -13.252947785.Subproblem 1
x + 12.625 = 13.252947785 Simplifying x + 12.625 = 13.252947785 Reorder the terms: 12.625 + x = 13.252947785 Solving 12.625 + x = 13.252947785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.625' to each side of the equation. 12.625 + -12.625 + x = 13.252947785 + -12.625 Combine like terms: 12.625 + -12.625 = 0.000 0.000 + x = 13.252947785 + -12.625 x = 13.252947785 + -12.625 Combine like terms: 13.252947785 + -12.625 = 0.627947785 x = 0.627947785 Simplifying x = 0.627947785Subproblem 2
x + 12.625 = -13.252947785 Simplifying x + 12.625 = -13.252947785 Reorder the terms: 12.625 + x = -13.252947785 Solving 12.625 + x = -13.252947785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.625' to each side of the equation. 12.625 + -12.625 + x = -13.252947785 + -12.625 Combine like terms: 12.625 + -12.625 = 0.000 0.000 + x = -13.252947785 + -12.625 x = -13.252947785 + -12.625 Combine like terms: -13.252947785 + -12.625 = -25.877947785 x = -25.877947785 Simplifying x = -25.877947785Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.627947785, -25.877947785}
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