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Simplifying 4x2 + -5x + -138 = 0 Reorder the terms: -138 + -5x + 4x2 = 0 Solving -138 + -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'. -34.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + -1.25x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + -1.25x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + -1.25x + x2 = 0 + 34.5 -1.25x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 -1.25x + x2 = 34.5 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 = 34.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 34.5 + 0.390625 Combine like terms: 34.5 + 0.390625 = 34.890625 0.390625 + -1.25x + x2 = 34.890625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 34.890625 Calculate the square root of the right side: 5.906828675 Break this problem into two subproblems by setting (x + -0.625) equal to 5.906828675 and -5.906828675.Subproblem 1
x + -0.625 = 5.906828675 Simplifying x + -0.625 = 5.906828675 Reorder the terms: -0.625 + x = 5.906828675 Solving -0.625 + x = 5.906828675 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 = 5.906828675 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 5.906828675 + 0.625 x = 5.906828675 + 0.625 Combine like terms: 5.906828675 + 0.625 = 6.531828675 x = 6.531828675 Simplifying x = 6.531828675Subproblem 2
x + -0.625 = -5.906828675 Simplifying x + -0.625 = -5.906828675 Reorder the terms: -0.625 + x = -5.906828675 Solving -0.625 + x = -5.906828675 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 = -5.906828675 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -5.906828675 + 0.625 x = -5.906828675 + 0.625 Combine like terms: -5.906828675 + 0.625 = -5.281828675 x = -5.281828675 Simplifying x = -5.281828675Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.531828675, -5.281828675}
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