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Simplifying 4x2 + -5x + -385 = 0 Reorder the terms: -385 + -5x + 4x2 = 0 Solving -385 + -5x + 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'. -96.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '96.25' to each side of the equation. -96.25 + -1.25x + 96.25 + x2 = 0 + 96.25 Reorder the terms: -96.25 + 96.25 + -1.25x + x2 = 0 + 96.25 Combine like terms: -96.25 + 96.25 = 0.00 0.00 + -1.25x + x2 = 0 + 96.25 -1.25x + x2 = 0 + 96.25 Combine like terms: 0 + 96.25 = 96.25 -1.25x + x2 = 96.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 96.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 96.25 + 0.390625 Combine like terms: 96.25 + 0.390625 = 96.640625 0.390625 + -1.25x + x2 = 96.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 96.640625 Calculate the square root of the right side: 9.830596371 Break this problem into two subproblems by setting (x + -0.625) equal to 9.830596371 and -9.830596371.Subproblem 1
x + -0.625 = 9.830596371 Simplifying x + -0.625 = 9.830596371 Reorder the terms: -0.625 + x = 9.830596371 Solving -0.625 + x = 9.830596371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 9.830596371 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 9.830596371 + 0.625 x = 9.830596371 + 0.625 Combine like terms: 9.830596371 + 0.625 = 10.455596371 x = 10.455596371 Simplifying x = 10.455596371Subproblem 2
x + -0.625 = -9.830596371 Simplifying x + -0.625 = -9.830596371 Reorder the terms: -0.625 + x = -9.830596371 Solving -0.625 + x = -9.830596371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -9.830596371 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -9.830596371 + 0.625 x = -9.830596371 + 0.625 Combine like terms: -9.830596371 + 0.625 = -9.205596371 x = -9.205596371 Simplifying x = -9.205596371Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.455596371, -9.205596371}
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