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Simplifying 4x2 + -5x + -119 = 0 Reorder the terms: -119 + -5x + 4x2 = 0 Solving -119 + -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'. -29.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '29.75' to each side of the equation. -29.75 + -1.25x + 29.75 + x2 = 0 + 29.75 Reorder the terms: -29.75 + 29.75 + -1.25x + x2 = 0 + 29.75 Combine like terms: -29.75 + 29.75 = 0.00 0.00 + -1.25x + x2 = 0 + 29.75 -1.25x + x2 = 0 + 29.75 Combine like terms: 0 + 29.75 = 29.75 -1.25x + x2 = 29.75 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 = 29.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 29.75 + 0.390625 Combine like terms: 29.75 + 0.390625 = 30.140625 0.390625 + -1.25x + x2 = 30.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 30.140625 Calculate the square root of the right side: 5.490047814 Break this problem into two subproblems by setting (x + -0.625) equal to 5.490047814 and -5.490047814.Subproblem 1
x + -0.625 = 5.490047814 Simplifying x + -0.625 = 5.490047814 Reorder the terms: -0.625 + x = 5.490047814 Solving -0.625 + x = 5.490047814 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 = 5.490047814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 5.490047814 + 0.625 x = 5.490047814 + 0.625 Combine like terms: 5.490047814 + 0.625 = 6.115047814 x = 6.115047814 Simplifying x = 6.115047814Subproblem 2
x + -0.625 = -5.490047814 Simplifying x + -0.625 = -5.490047814 Reorder the terms: -0.625 + x = -5.490047814 Solving -0.625 + x = -5.490047814 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 = -5.490047814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -5.490047814 + 0.625 x = -5.490047814 + 0.625 Combine like terms: -5.490047814 + 0.625 = -4.865047814 x = -4.865047814 Simplifying x = -4.865047814Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.115047814, -4.865047814}
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