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Simplifying -2x2 + 10x + 1 = 0 Reorder the terms: 1 + 10x + -2x2 = 0 Solving 1 + 10x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5x + x2 = 0 + 0.5 -5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5x + x2 = 0.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.5 + 6.25 Combine like terms: 0.5 + 6.25 = 6.75 6.25 + -5x + x2 = 6.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -2.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -2.5 = 2.598076211 Simplifying x + -2.5 = 2.598076211 Reorder the terms: -2.5 + x = 2.598076211 Solving -2.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.598076211 + 2.5 x = 2.598076211 + 2.5 Combine like terms: 2.598076211 + 2.5 = 5.098076211 x = 5.098076211 Simplifying x = 5.098076211Subproblem 2
x + -2.5 = -2.598076211 Simplifying x + -2.5 = -2.598076211 Reorder the terms: -2.5 + x = -2.598076211 Solving -2.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.598076211 + 2.5 x = -2.598076211 + 2.5 Combine like terms: -2.598076211 + 2.5 = -0.098076211 x = -0.098076211 Simplifying x = -0.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.098076211, -0.098076211}
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