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Simplifying 0 = 4x2 + 5x + -245 Reorder the terms: 0 = -245 + 5x + 4x2 Solving 0 = -245 + 5x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 245 = 245 245 + -5x + -4x2 = -245 + 5x + 4x2 + 245 + -5x + -4x2 Reorder the terms: 245 + -5x + -4x2 = -245 + 245 + 5x + -5x + 4x2 + -4x2 Combine like terms: -245 + 245 = 0 245 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 245 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 245 + -5x + -4x2 = 0 + 4x2 + -4x2 245 + -5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 245 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -61.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '61.25' to each side of the equation. -61.25 + 1.25x + 61.25 + x2 = 0 + 61.25 Reorder the terms: -61.25 + 61.25 + 1.25x + x2 = 0 + 61.25 Combine like terms: -61.25 + 61.25 = 0.00 0.00 + 1.25x + x2 = 0 + 61.25 1.25x + x2 = 0 + 61.25 Combine like terms: 0 + 61.25 = 61.25 1.25x + x2 = 61.25 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 = 61.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 61.25 + 0.390625 Combine like terms: 61.25 + 0.390625 = 61.640625 0.390625 + 1.25x + x2 = 61.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 61.640625 Calculate the square root of the right side: 7.851154374 Break this problem into two subproblems by setting (x + 0.625) equal to 7.851154374 and -7.851154374.Subproblem 1
x + 0.625 = 7.851154374 Simplifying x + 0.625 = 7.851154374 Reorder the terms: 0.625 + x = 7.851154374 Solving 0.625 + x = 7.851154374 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 = 7.851154374 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 7.851154374 + -0.625 x = 7.851154374 + -0.625 Combine like terms: 7.851154374 + -0.625 = 7.226154374 x = 7.226154374 Simplifying x = 7.226154374Subproblem 2
x + 0.625 = -7.851154374 Simplifying x + 0.625 = -7.851154374 Reorder the terms: 0.625 + x = -7.851154374 Solving 0.625 + x = -7.851154374 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 = -7.851154374 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -7.851154374 + -0.625 x = -7.851154374 + -0.625 Combine like terms: -7.851154374 + -0.625 = -8.476154374 x = -8.476154374 Simplifying x = -8.476154374Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.226154374, -8.476154374}
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