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Simplifying 10x2 + -19x + -139 = 0 Reorder the terms: -139 + -19x + 10x2 = 0 Solving -139 + -19x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -13.9 + -1.9x + x2 = 0 Move the constant term to the right: Add '13.9' to each side of the equation. -13.9 + -1.9x + 13.9 + x2 = 0 + 13.9 Reorder the terms: -13.9 + 13.9 + -1.9x + x2 = 0 + 13.9 Combine like terms: -13.9 + 13.9 = 0.0 0.0 + -1.9x + x2 = 0 + 13.9 -1.9x + x2 = 0 + 13.9 Combine like terms: 0 + 13.9 = 13.9 -1.9x + x2 = 13.9 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = 13.9 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = 13.9 + 0.9025 Combine like terms: 13.9 + 0.9025 = 14.8025 0.9025 + -1.9x + x2 = 14.8025 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 14.8025 Calculate the square root of the right side: 3.847401721 Break this problem into two subproblems by setting (x + -0.95) equal to 3.847401721 and -3.847401721.Subproblem 1
x + -0.95 = 3.847401721 Simplifying x + -0.95 = 3.847401721 Reorder the terms: -0.95 + x = 3.847401721 Solving -0.95 + x = 3.847401721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 3.847401721 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 3.847401721 + 0.95 x = 3.847401721 + 0.95 Combine like terms: 3.847401721 + 0.95 = 4.797401721 x = 4.797401721 Simplifying x = 4.797401721Subproblem 2
x + -0.95 = -3.847401721 Simplifying x + -0.95 = -3.847401721 Reorder the terms: -0.95 + x = -3.847401721 Solving -0.95 + x = -3.847401721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -3.847401721 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -3.847401721 + 0.95 x = -3.847401721 + 0.95 Combine like terms: -3.847401721 + 0.95 = -2.897401721 x = -2.897401721 Simplifying x = -2.897401721Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.797401721, -2.897401721}
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