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Simplifying 14x2 + 27x + 6 = 0 Reorder the terms: 6 + 27x + 14x2 = 0 Solving 6 + 27x + 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'. 0.4285714286 + 1.928571429x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 1.928571429x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 1.928571429x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 1.928571429x + x2 = 0 + -0.4285714286 1.928571429x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 1.928571429x + x2 = -0.4285714286 The x term is 1.928571429x. Take half its coefficient (0.9642857145). Square it (0.9298469392) and add it to both sides. Add '0.9298469392' to each side of the equation. 1.928571429x + 0.9298469392 + x2 = -0.4285714286 + 0.9298469392 Reorder the terms: 0.9298469392 + 1.928571429x + x2 = -0.4285714286 + 0.9298469392 Combine like terms: -0.4285714286 + 0.9298469392 = 0.5012755106 0.9298469392 + 1.928571429x + x2 = 0.5012755106 Factor a perfect square on the left side: (x + 0.9642857145)(x + 0.9642857145) = 0.5012755106 Calculate the square root of the right side: 0.708008129 Break this problem into two subproblems by setting (x + 0.9642857145) equal to 0.708008129 and -0.708008129.Subproblem 1
x + 0.9642857145 = 0.708008129 Simplifying x + 0.9642857145 = 0.708008129 Reorder the terms: 0.9642857145 + x = 0.708008129 Solving 0.9642857145 + x = 0.708008129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9642857145' to each side of the equation. 0.9642857145 + -0.9642857145 + x = 0.708008129 + -0.9642857145 Combine like terms: 0.9642857145 + -0.9642857145 = 0.0000000000 0.0000000000 + x = 0.708008129 + -0.9642857145 x = 0.708008129 + -0.9642857145 Combine like terms: 0.708008129 + -0.9642857145 = -0.2562775855 x = -0.2562775855 Simplifying x = -0.2562775855Subproblem 2
x + 0.9642857145 = -0.708008129 Simplifying x + 0.9642857145 = -0.708008129 Reorder the terms: 0.9642857145 + x = -0.708008129 Solving 0.9642857145 + x = -0.708008129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9642857145' to each side of the equation. 0.9642857145 + -0.9642857145 + x = -0.708008129 + -0.9642857145 Combine like terms: 0.9642857145 + -0.9642857145 = 0.0000000000 0.0000000000 + x = -0.708008129 + -0.9642857145 x = -0.708008129 + -0.9642857145 Combine like terms: -0.708008129 + -0.9642857145 = -1.6722938435 x = -1.6722938435 Simplifying x = -1.6722938435Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2562775855, -1.6722938435}
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