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Simplifying 14x2 + 19x + -8 = 0 Reorder the terms: -8 + 19x + 14x2 = 0 Solving -8 + 19x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.5714285714 + 1.357142857x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 1.357142857x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 1.357142857x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 1.357142857x + x2 = 0 + 0.5714285714 1.357142857x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 1.357142857x + x2 = 0.5714285714 The x term is 1.357142857x. Take half its coefficient (0.6785714285). Square it (0.4604591836) and add it to both sides. Add '0.4604591836' to each side of the equation. 1.357142857x + 0.4604591836 + x2 = 0.5714285714 + 0.4604591836 Reorder the terms: 0.4604591836 + 1.357142857x + x2 = 0.5714285714 + 0.4604591836 Combine like terms: 0.5714285714 + 0.4604591836 = 1.031887755 0.4604591836 + 1.357142857x + x2 = 1.031887755 Factor a perfect square on the left side: (x + 0.6785714285)(x + 0.6785714285) = 1.031887755 Calculate the square root of the right side: 1.015818761 Break this problem into two subproblems by setting (x + 0.6785714285) equal to 1.015818761 and -1.015818761.Subproblem 1
x + 0.6785714285 = 1.015818761 Simplifying x + 0.6785714285 = 1.015818761 Reorder the terms: 0.6785714285 + x = 1.015818761 Solving 0.6785714285 + x = 1.015818761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6785714285' to each side of the equation. 0.6785714285 + -0.6785714285 + x = 1.015818761 + -0.6785714285 Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000 0.0000000000 + x = 1.015818761 + -0.6785714285 x = 1.015818761 + -0.6785714285 Combine like terms: 1.015818761 + -0.6785714285 = 0.3372473325 x = 0.3372473325 Simplifying x = 0.3372473325Subproblem 2
x + 0.6785714285 = -1.015818761 Simplifying x + 0.6785714285 = -1.015818761 Reorder the terms: 0.6785714285 + x = -1.015818761 Solving 0.6785714285 + x = -1.015818761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6785714285' to each side of the equation. 0.6785714285 + -0.6785714285 + x = -1.015818761 + -0.6785714285 Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000 0.0000000000 + x = -1.015818761 + -0.6785714285 x = -1.015818761 + -0.6785714285 Combine like terms: -1.015818761 + -0.6785714285 = -1.6943901895 x = -1.6943901895 Simplifying x = -1.6943901895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3372473325, -1.6943901895}
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