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Simplifying 13x2 + -8x + 1 = 0 Reorder the terms: 1 + -8x + 13x2 = 0 Solving 1 + -8x + 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 + -0.6153846154x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + -0.6153846154x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + -0.6153846154x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + -0.6153846154x + x2 = 0 + -0.07692307692 -0.6153846154x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 -0.6153846154x + x2 = -0.07692307692 The x term is -0.6153846154x. Take half its coefficient (-0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. -0.6153846154x + 0.09467455622 + x2 = -0.07692307692 + 0.09467455622 Reorder the terms: 0.09467455622 + -0.6153846154x + x2 = -0.07692307692 + 0.09467455622 Combine like terms: -0.07692307692 + 0.09467455622 = 0.0177514793 0.09467455622 + -0.6153846154x + x2 = 0.0177514793 Factor a perfect square on the left side: (x + -0.3076923077)(x + -0.3076923077) = 0.0177514793 Calculate the square root of the right side: 0.133234678 Break this problem into two subproblems by setting (x + -0.3076923077) equal to 0.133234678 and -0.133234678.Subproblem 1
x + -0.3076923077 = 0.133234678 Simplifying x + -0.3076923077 = 0.133234678 Reorder the terms: -0.3076923077 + x = 0.133234678 Solving -0.3076923077 + x = 0.133234678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = 0.133234678 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = 0.133234678 + 0.3076923077 x = 0.133234678 + 0.3076923077 Combine like terms: 0.133234678 + 0.3076923077 = 0.4409269857 x = 0.4409269857 Simplifying x = 0.4409269857Subproblem 2
x + -0.3076923077 = -0.133234678 Simplifying x + -0.3076923077 = -0.133234678 Reorder the terms: -0.3076923077 + x = -0.133234678 Solving -0.3076923077 + x = -0.133234678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = -0.133234678 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = -0.133234678 + 0.3076923077 x = -0.133234678 + 0.3076923077 Combine like terms: -0.133234678 + 0.3076923077 = 0.1744576297 x = 0.1744576297 Simplifying x = 0.1744576297Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4409269857, 0.1744576297}
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