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Simplifying 4x2 + -85x + -2 = 0 Reorder the terms: -2 + -85x + 4x2 = 0 Solving -2 + -85x + 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'. -0.5 + -21.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -21.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -21.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -21.25x + x2 = 0 + 0.5 -21.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -21.25x + x2 = 0.5 The x term is -21.25x. Take half its coefficient (-10.625). Square it (112.890625) and add it to both sides. Add '112.890625' to each side of the equation. -21.25x + 112.890625 + x2 = 0.5 + 112.890625 Reorder the terms: 112.890625 + -21.25x + x2 = 0.5 + 112.890625 Combine like terms: 0.5 + 112.890625 = 113.390625 112.890625 + -21.25x + x2 = 113.390625 Factor a perfect square on the left side: (x + -10.625)(x + -10.625) = 113.390625 Calculate the square root of the right side: 10.648503416 Break this problem into two subproblems by setting (x + -10.625) equal to 10.648503416 and -10.648503416.Subproblem 1
x + -10.625 = 10.648503416 Simplifying x + -10.625 = 10.648503416 Reorder the terms: -10.625 + x = 10.648503416 Solving -10.625 + x = 10.648503416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = 10.648503416 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = 10.648503416 + 10.625 x = 10.648503416 + 10.625 Combine like terms: 10.648503416 + 10.625 = 21.273503416 x = 21.273503416 Simplifying x = 21.273503416Subproblem 2
x + -10.625 = -10.648503416 Simplifying x + -10.625 = -10.648503416 Reorder the terms: -10.625 + x = -10.648503416 Solving -10.625 + x = -10.648503416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = -10.648503416 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = -10.648503416 + 10.625 x = -10.648503416 + 10.625 Combine like terms: -10.648503416 + 10.625 = -0.023503416 x = -0.023503416 Simplifying x = -0.023503416Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.273503416, -0.023503416}
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