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Simplifying 10x2 + -5x + -14 = 0 Reorder the terms: -14 + -5x + 10x2 = 0 Solving -14 + -5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.4 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.5x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.5x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.5x + x2 = 0 + 1.4 -0.5x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.5x + x2 = 1.4 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.4 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.4 + 0.0625 Combine like terms: 1.4 + 0.0625 = 1.4625 0.0625 + -0.5x + x2 = 1.4625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.4625 Calculate the square root of the right side: 1.209338662 Break this problem into two subproblems by setting (x + -0.25) equal to 1.209338662 and -1.209338662.Subproblem 1
x + -0.25 = 1.209338662 Simplifying x + -0.25 = 1.209338662 Reorder the terms: -0.25 + x = 1.209338662 Solving -0.25 + x = 1.209338662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.209338662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.209338662 + 0.25 x = 1.209338662 + 0.25 Combine like terms: 1.209338662 + 0.25 = 1.459338662 x = 1.459338662 Simplifying x = 1.459338662Subproblem 2
x + -0.25 = -1.209338662 Simplifying x + -0.25 = -1.209338662 Reorder the terms: -0.25 + x = -1.209338662 Solving -0.25 + x = -1.209338662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.209338662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.209338662 + 0.25 x = -1.209338662 + 0.25 Combine like terms: -1.209338662 + 0.25 = -0.959338662 x = -0.959338662 Simplifying x = -0.959338662Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.459338662, -0.959338662}
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