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Simplifying 3x2 = 40x + 246 Reorder the terms: 3x2 = 246 + 40x Solving 3x2 = 246 + 40x Solving for variable 'x'. Reorder the terms: -246 + -40x + 3x2 = 246 + 40x + -246 + -40x Reorder the terms: -246 + -40x + 3x2 = 246 + -246 + 40x + -40x Combine like terms: 246 + -246 = 0 -246 + -40x + 3x2 = 0 + 40x + -40x -246 + -40x + 3x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -246 + -40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -82 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '82' to each side of the equation. -82 + -13.33333333x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + -13.33333333x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -13.33333333x + x2 = 0 + 82 -13.33333333x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 -13.33333333x + x2 = 82 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 82 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 82 + 44.44444442 Combine like terms: 82 + 44.44444442 = 126.44444442 44.44444442 + -13.33333333x + x2 = 126.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 126.44444442 Calculate the square root of the right side: 11.244751861 Break this problem into two subproblems by setting (x + -6.666666665) equal to 11.244751861 and -11.244751861.Subproblem 1
x + -6.666666665 = 11.244751861 Simplifying x + -6.666666665 = 11.244751861 Reorder the terms: -6.666666665 + x = 11.244751861 Solving -6.666666665 + x = 11.244751861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 11.244751861 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 11.244751861 + 6.666666665 x = 11.244751861 + 6.666666665 Combine like terms: 11.244751861 + 6.666666665 = 17.911418526 x = 17.911418526 Simplifying x = 17.911418526Subproblem 2
x + -6.666666665 = -11.244751861 Simplifying x + -6.666666665 = -11.244751861 Reorder the terms: -6.666666665 + x = -11.244751861 Solving -6.666666665 + x = -11.244751861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -11.244751861 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -11.244751861 + 6.666666665 x = -11.244751861 + 6.666666665 Combine like terms: -11.244751861 + 6.666666665 = -4.578085196 x = -4.578085196 Simplifying x = -4.578085196Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.911418526, -4.578085196}
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