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Simplifying 0 = 13x2 + -13x + 1 Reorder the terms: 0 = 1 + -13x + 13x2 Solving 0 = 1 + -13x + 13x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 13x + -13x2 = 1 + -13x + 13x2 + -1 + 13x + -13x2 Reorder the terms: -1 + 13x + -13x2 = 1 + -1 + -13x + 13x + 13x2 + -13x2 Combine like terms: 1 + -1 = 0 -1 + 13x + -13x2 = 0 + -13x + 13x + 13x2 + -13x2 -1 + 13x + -13x2 = -13x + 13x + 13x2 + -13x2 Combine like terms: -13x + 13x = 0 -1 + 13x + -13x2 = 0 + 13x2 + -13x2 -1 + 13x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -1 + 13x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 0.07692307692 + -1x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + -1x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + -1x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + -0.07692307692 -1x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 -1x + x2 = -0.07692307692 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 = -0.07692307692 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.07692307692 + 0.25 Combine like terms: -0.07692307692 + 0.25 = 0.17307692308 0.25 + -1x + x2 = 0.17307692308 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.17307692308 Calculate the square root of the right side: 0.416025147 Break this problem into two subproblems by setting (x + -0.5) equal to 0.416025147 and -0.416025147.Subproblem 1
x + -0.5 = 0.416025147 Simplifying x + -0.5 = 0.416025147 Reorder the terms: -0.5 + x = 0.416025147 Solving -0.5 + x = 0.416025147 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 = 0.416025147 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.416025147 + 0.5 x = 0.416025147 + 0.5 Combine like terms: 0.416025147 + 0.5 = 0.916025147 x = 0.916025147 Simplifying x = 0.916025147Subproblem 2
x + -0.5 = -0.416025147 Simplifying x + -0.5 = -0.416025147 Reorder the terms: -0.5 + x = -0.416025147 Solving -0.5 + x = -0.416025147 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 = -0.416025147 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.416025147 + 0.5 x = -0.416025147 + 0.5 Combine like terms: -0.416025147 + 0.5 = 0.083974853 x = 0.083974853 Simplifying x = 0.083974853Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.916025147, 0.083974853}
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