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Simplifying 14x2 + -19x + -9 = 0 Reorder the terms: -9 + -19x + 14x2 = 0 Solving -9 + -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'. -0.6428571429 + -1.357142857x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -1.357142857x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -1.357142857x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -1.357142857x + x2 = 0 + 0.6428571429 -1.357142857x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -1.357142857x + x2 = 0.6428571429 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 = 0.6428571429 + 0.4604591836 Reorder the terms: 0.4604591836 + -1.357142857x + x2 = 0.6428571429 + 0.4604591836 Combine like terms: 0.6428571429 + 0.4604591836 = 1.1033163265 0.4604591836 + -1.357142857x + x2 = 1.1033163265 Factor a perfect square on the left side: (x + -0.6785714285)(x + -0.6785714285) = 1.1033163265 Calculate the square root of the right side: 1.050388655 Break this problem into two subproblems by setting (x + -0.6785714285) equal to 1.050388655 and -1.050388655.Subproblem 1
x + -0.6785714285 = 1.050388655 Simplifying x + -0.6785714285 = 1.050388655 Reorder the terms: -0.6785714285 + x = 1.050388655 Solving -0.6785714285 + x = 1.050388655 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 = 1.050388655 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = 1.050388655 + 0.6785714285 x = 1.050388655 + 0.6785714285 Combine like terms: 1.050388655 + 0.6785714285 = 1.7289600835 x = 1.7289600835 Simplifying x = 1.7289600835Subproblem 2
x + -0.6785714285 = -1.050388655 Simplifying x + -0.6785714285 = -1.050388655 Reorder the terms: -0.6785714285 + x = -1.050388655 Solving -0.6785714285 + x = -1.050388655 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 = -1.050388655 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = -1.050388655 + 0.6785714285 x = -1.050388655 + 0.6785714285 Combine like terms: -1.050388655 + 0.6785714285 = -0.3718172265 x = -0.3718172265 Simplifying x = -0.3718172265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7289600835, -0.3718172265}
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