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Simplifying 10x2 + -1x + -14 = 0 Reorder the terms: -14 + -1x + 10x2 = 0 Solving -14 + -1x + 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 + -0.1x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.1x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.1x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.1x + x2 = 0 + 1.4 -0.1x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.1x + x2 = 1.4 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 1.4 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 1.4 + 0.0025 Combine like terms: 1.4 + 0.0025 = 1.4025 0.0025 + -0.1x + x2 = 1.4025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (x + -0.05) equal to 1.184271928 and -1.184271928.Subproblem 1
x + -0.05 = 1.184271928 Simplifying x + -0.05 = 1.184271928 Reorder the terms: -0.05 + x = 1.184271928 Solving -0.05 + x = 1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.184271928 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.184271928 + 0.05 x = 1.184271928 + 0.05 Combine like terms: 1.184271928 + 0.05 = 1.234271928 x = 1.234271928 Simplifying x = 1.234271928Subproblem 2
x + -0.05 = -1.184271928 Simplifying x + -0.05 = -1.184271928 Reorder the terms: -0.05 + x = -1.184271928 Solving -0.05 + x = -1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.184271928 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.184271928 + 0.05 x = -1.184271928 + 0.05 Combine like terms: -1.184271928 + 0.05 = -1.134271928 x = -1.134271928 Simplifying x = -1.134271928Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.234271928, -1.134271928}
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