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Simplifying 14x2 + -21x + -8 = 0 Reorder the terms: -8 + -21x + 14x2 = 0 Solving -8 + -21x + 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 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1.5x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1.5x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.5714285714 -1.5x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1.5x + x2 = 0.5714285714 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.5714285714 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.5714285714 + 0.5625 Combine like terms: 0.5714285714 + 0.5625 = 1.1339285714 0.5625 + -1.5x + x2 = 1.1339285714 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.1339285714 Calculate the square root of the right side: 1.064860823 Break this problem into two subproblems by setting (x + -0.75) equal to 1.064860823 and -1.064860823.Subproblem 1
x + -0.75 = 1.064860823 Simplifying x + -0.75 = 1.064860823 Reorder the terms: -0.75 + x = 1.064860823 Solving -0.75 + x = 1.064860823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.064860823 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.064860823 + 0.75 x = 1.064860823 + 0.75 Combine like terms: 1.064860823 + 0.75 = 1.814860823 x = 1.814860823 Simplifying x = 1.814860823Subproblem 2
x + -0.75 = -1.064860823 Simplifying x + -0.75 = -1.064860823 Reorder the terms: -0.75 + x = -1.064860823 Solving -0.75 + x = -1.064860823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.064860823 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.064860823 + 0.75 x = -1.064860823 + 0.75 Combine like terms: -1.064860823 + 0.75 = -0.314860823 x = -0.314860823 Simplifying x = -0.314860823Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.814860823, -0.314860823}
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