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Simplifying 4x2 + -5x + -57 = 0 Reorder the terms: -57 + -5x + 4x2 = 0 Solving -57 + -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'. -14.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '14.25' to each side of the equation. -14.25 + -1.25x + 14.25 + x2 = 0 + 14.25 Reorder the terms: -14.25 + 14.25 + -1.25x + x2 = 0 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + -1.25x + x2 = 0 + 14.25 -1.25x + x2 = 0 + 14.25 Combine like terms: 0 + 14.25 = 14.25 -1.25x + x2 = 14.25 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 = 14.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 14.25 + 0.390625 Combine like terms: 14.25 + 0.390625 = 14.640625 0.390625 + -1.25x + x2 = 14.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 14.640625 Calculate the square root of the right side: 3.826306966 Break this problem into two subproblems by setting (x + -0.625) equal to 3.826306966 and -3.826306966.Subproblem 1
x + -0.625 = 3.826306966 Simplifying x + -0.625 = 3.826306966 Reorder the terms: -0.625 + x = 3.826306966 Solving -0.625 + x = 3.826306966 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 = 3.826306966 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.826306966 + 0.625 x = 3.826306966 + 0.625 Combine like terms: 3.826306966 + 0.625 = 4.451306966 x = 4.451306966 Simplifying x = 4.451306966Subproblem 2
x + -0.625 = -3.826306966 Simplifying x + -0.625 = -3.826306966 Reorder the terms: -0.625 + x = -3.826306966 Solving -0.625 + x = -3.826306966 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 = -3.826306966 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.826306966 + 0.625 x = -3.826306966 + 0.625 Combine like terms: -3.826306966 + 0.625 = -3.201306966 x = -3.201306966 Simplifying x = -3.201306966Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.451306966, -3.201306966}
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