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Simplifying 13x2 + -13x + -10 = 0 Reorder the terms: -10 + -13x + 13x2 = 0 Solving -10 + -13x + 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'. -0.7692307692 + -1x + x2 = 0 Move the constant term to the right: Add '0.7692307692' to each side of the equation. -0.7692307692 + -1x + 0.7692307692 + x2 = 0 + 0.7692307692 Reorder the terms: -0.7692307692 + 0.7692307692 + -1x + x2 = 0 + 0.7692307692 Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.7692307692 -1x + x2 = 0 + 0.7692307692 Combine like terms: 0 + 0.7692307692 = 0.7692307692 -1x + x2 = 0.7692307692 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 = 0.7692307692 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.7692307692 + 0.25 Combine like terms: 0.7692307692 + 0.25 = 1.0192307692 0.25 + -1x + x2 = 1.0192307692 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.0192307692 Calculate the square root of the right side: 1.009569596 Break this problem into two subproblems by setting (x + -0.5) equal to 1.009569596 and -1.009569596.Subproblem 1
x + -0.5 = 1.009569596 Simplifying x + -0.5 = 1.009569596 Reorder the terms: -0.5 + x = 1.009569596 Solving -0.5 + x = 1.009569596 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 = 1.009569596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.009569596 + 0.5 x = 1.009569596 + 0.5 Combine like terms: 1.009569596 + 0.5 = 1.509569596 x = 1.509569596 Simplifying x = 1.509569596Subproblem 2
x + -0.5 = -1.009569596 Simplifying x + -0.5 = -1.009569596 Reorder the terms: -0.5 + x = -1.009569596 Solving -0.5 + x = -1.009569596 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 = -1.009569596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.009569596 + 0.5 x = -1.009569596 + 0.5 Combine like terms: -1.009569596 + 0.5 = -0.509569596 x = -0.509569596 Simplifying x = -0.509569596Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.509569596, -0.509569596}
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