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Simplifying 6x2 + -18x + 13 = 0 Reorder the terms: 13 + -18x + 6x2 = 0 Solving 13 + -18x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + -3x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + -3x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + -3x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + -2.166666667 -3x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 -3x + x2 = -2.166666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.166666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.166666667 + 2.25 Combine like terms: -2.166666667 + 2.25 = 0.083333333 2.25 + -3x + x2 = 0.083333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.083333333 Calculate the square root of the right side: 0.288675134 Break this problem into two subproblems by setting (x + -1.5) equal to 0.288675134 and -0.288675134.Subproblem 1
x + -1.5 = 0.288675134 Simplifying x + -1.5 = 0.288675134 Reorder the terms: -1.5 + x = 0.288675134 Solving -1.5 + x = 0.288675134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.288675134 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.288675134 + 1.5 x = 0.288675134 + 1.5 Combine like terms: 0.288675134 + 1.5 = 1.788675134 x = 1.788675134 Simplifying x = 1.788675134Subproblem 2
x + -1.5 = -0.288675134 Simplifying x + -1.5 = -0.288675134 Reorder the terms: -1.5 + x = -0.288675134 Solving -1.5 + x = -0.288675134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.288675134 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.288675134 + 1.5 x = -0.288675134 + 1.5 Combine like terms: -0.288675134 + 1.5 = 1.211324866 x = 1.211324866 Simplifying x = 1.211324866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.788675134, 1.211324866}
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