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Simplifying 13x2 + x + -1 = 0 Reorder the terms: -1 + x + 13x2 = 0 Solving -1 + x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.07692307692 + 0.07692307692x + x2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + 0.07692307692x + 0.07692307692 + x2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + 0.07692307692x + x2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + 0.07692307692x + x2 = 0 + 0.07692307692 0.07692307692x + x2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 0.07692307692x + x2 = 0.07692307692 The x term is x. 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. 0.07692307692x + 0.25 + x2 = 0.07692307692 + 0.25 Reorder the terms: 0.25 + 0.07692307692x + x2 = 0.07692307692 + 0.25 Combine like terms: 0.07692307692 + 0.25 = 0.32692307692 0.25 + 0.07692307692x + x2 = 0.32692307692 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.32692307692 Calculate the square root of the right side: 0.571771875 Break this problem into two subproblems by setting (x + 0.5) equal to 0.571771875 and -0.571771875.Subproblem 1
x + 0.5 = 0.571771875 Simplifying x + 0.5 = 0.571771875 Reorder the terms: 0.5 + x = 0.571771875 Solving 0.5 + x = 0.571771875 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 = 0.571771875 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.571771875 + -0.5 x = 0.571771875 + -0.5 Combine like terms: 0.571771875 + -0.5 = 0.071771875 x = 0.071771875 Simplifying x = 0.071771875Subproblem 2
x + 0.5 = -0.571771875 Simplifying x + 0.5 = -0.571771875 Reorder the terms: 0.5 + x = -0.571771875 Solving 0.5 + x = -0.571771875 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 = -0.571771875 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.571771875 + -0.5 x = -0.571771875 + -0.5 Combine like terms: -0.571771875 + -0.5 = -1.071771875 x = -1.071771875 Simplifying x = -1.071771875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.071771875, -1.071771875}
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