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Simplifying 0 = 6x2 + 6x + -13 Reorder the terms: 0 = -13 + 6x + 6x2 Solving 0 = -13 + 6x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 13 = 13 13 + -6x + -6x2 = -13 + 6x + 6x2 + 13 + -6x + -6x2 Reorder the terms: 13 + -6x + -6x2 = -13 + 13 + 6x + -6x + 6x2 + -6x2 Combine like terms: -13 + 13 = 0 13 + -6x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2 13 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 13 + -6x + -6x2 = 0 + 6x2 + -6x2 13 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 13 + -6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.166666667 + x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x + x2 = 0 + 2.166666667 x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 x + x2 = 2.166666667 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 = 2.166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.166666667 + 0.25 Combine like terms: 2.166666667 + 0.25 = 2.416666667 1.25 + x2 = 2.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.416666667 Calculate the square root of the right side: 1.554563176 Break this problem into two subproblems by setting (x + 0.5) equal to 1.554563176 and -1.554563176.Subproblem 1
x + 0.5 = 1.554563176 Simplifying x + 0.5 = 1.554563176 Reorder the terms: 0.5 + x = 1.554563176 Solving 0.5 + x = 1.554563176 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 = 1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.554563176 + -0.5 x = 1.554563176 + -0.5 Combine like terms: 1.554563176 + -0.5 = 1.054563176 x = 1.054563176 Simplifying x = 1.054563176Subproblem 2
x + 0.5 = -1.554563176 Simplifying x + 0.5 = -1.554563176 Reorder the terms: 0.5 + x = -1.554563176 Solving 0.5 + x = -1.554563176 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 = -1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.554563176 + -0.5 x = -1.554563176 + -0.5 Combine like terms: -1.554563176 + -0.5 = -2.054563176 x = -2.054563176 Simplifying x = -2.054563176Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.054563176, -2.054563176}
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