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Simplifying 10x2 + -10x + -1 = 0 Reorder the terms: -1 + -10x + 10x2 = 0 Solving -1 + -10x + 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'. -0.1 + -1x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -1x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -1x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -1x + x2 = 0 + 0.1 -1x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -1x + x2 = 0.1 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1 + 0.25 Combine like terms: 0.1 + 0.25 = 0.35 0.25 + -1x + x2 = 0.35 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.35 Calculate the square root of the right side: 0.591607978 Break this problem into two subproblems by setting (x + -0.5) equal to 0.591607978 and -0.591607978.Subproblem 1
x + -0.5 = 0.591607978 Simplifying x + -0.5 = 0.591607978 Reorder the terms: -0.5 + x = 0.591607978 Solving -0.5 + x = 0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.591607978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.591607978 + 0.5 x = 0.591607978 + 0.5 Combine like terms: 0.591607978 + 0.5 = 1.091607978 x = 1.091607978 Simplifying x = 1.091607978Subproblem 2
x + -0.5 = -0.591607978 Simplifying x + -0.5 = -0.591607978 Reorder the terms: -0.5 + x = -0.591607978 Solving -0.5 + x = -0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.591607978 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.591607978 + 0.5 x = -0.591607978 + 0.5 Combine like terms: -0.591607978 + 0.5 = -0.091607978 x = -0.091607978 Simplifying x = -0.091607978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.091607978, -0.091607978}
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