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Simplifying 13x2 + 13x = 6 Reorder the terms: 13x + 13x2 = 6 Solving 13x + 13x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 13x + 13x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 13x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.4615384615 + x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.4615384615 x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 x + x2 = 0.4615384615 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. + 0.25 + x2 = 0.4615384615 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.4615384615 + 0.25 Combine like terms: 0.4615384615 + 0.25 = 0.7115384615 1.25 + x2 = 0.7115384615 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.7115384615 Calculate the square root of the right side: 0.843527392 Break this problem into two subproblems by setting (x + 0.5) equal to 0.843527392 and -0.843527392.Subproblem 1
x + 0.5 = 0.843527392 Simplifying x + 0.5 = 0.843527392 Reorder the terms: 0.5 + x = 0.843527392 Solving 0.5 + x = 0.843527392 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 = 0.843527392 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.843527392 + -0.5 x = 0.843527392 + -0.5 Combine like terms: 0.843527392 + -0.5 = 0.343527392 x = 0.343527392 Simplifying x = 0.343527392Subproblem 2
x + 0.5 = -0.843527392 Simplifying x + 0.5 = -0.843527392 Reorder the terms: 0.5 + x = -0.843527392 Solving 0.5 + x = -0.843527392 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 = -0.843527392 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.843527392 + -0.5 x = -0.843527392 + -0.5 Combine like terms: -0.843527392 + -0.5 = -1.343527392 x = -1.343527392 Simplifying x = -1.343527392Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.343527392, -1.343527392}
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