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Simplifying 4 + 14x2 + -19x = 0 Reorder the terms: 4 + -19x + 14x2 = 0 Solving 4 + -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'. 0.2857142857 + -1.357142857x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.357142857x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.357142857x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.357142857x + x2 = 0 + -0.2857142857 -1.357142857x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.357142857x + x2 = -0.2857142857 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 = -0.2857142857 + 0.4604591836 Reorder the terms: 0.4604591836 + -1.357142857x + x2 = -0.2857142857 + 0.4604591836 Combine like terms: -0.2857142857 + 0.4604591836 = 0.1747448979 0.4604591836 + -1.357142857x + x2 = 0.1747448979 Factor a perfect square on the left side: (x + -0.6785714285)(x + -0.6785714285) = 0.1747448979 Calculate the square root of the right side: 0.418024997 Break this problem into two subproblems by setting (x + -0.6785714285) equal to 0.418024997 and -0.418024997.Subproblem 1
x + -0.6785714285 = 0.418024997 Simplifying x + -0.6785714285 = 0.418024997 Reorder the terms: -0.6785714285 + x = 0.418024997 Solving -0.6785714285 + x = 0.418024997 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 = 0.418024997 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = 0.418024997 + 0.6785714285 x = 0.418024997 + 0.6785714285 Combine like terms: 0.418024997 + 0.6785714285 = 1.0965964255 x = 1.0965964255 Simplifying x = 1.0965964255Subproblem 2
x + -0.6785714285 = -0.418024997 Simplifying x + -0.6785714285 = -0.418024997 Reorder the terms: -0.6785714285 + x = -0.418024997 Solving -0.6785714285 + x = -0.418024997 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 = -0.418024997 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = -0.418024997 + 0.6785714285 x = -0.418024997 + 0.6785714285 Combine like terms: -0.418024997 + 0.6785714285 = 0.2605464315 x = 0.2605464315 Simplifying x = 0.2605464315Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0965964255, 0.2605464315}
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