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Simplifying 3x2 + -38x + -84 = 0 Reorder the terms: -84 + -38x + 3x2 = 0 Solving -84 + -38x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -28 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -12.66666667x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -12.66666667x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -12.66666667x + x2 = 0 + 28 -12.66666667x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -12.66666667x + x2 = 28 The x term is -12.66666667x. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667x + 40.11111113 + x2 = 28 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = 28 + 40.11111113 Combine like terms: 28 + 40.11111113 = 68.11111113 40.11111113 + -12.66666667x + x2 = 68.11111113 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 68.11111113 Calculate the square root of the right side: 8.252945603 Break this problem into two subproblems by setting (x + -6.333333335) equal to 8.252945603 and -8.252945603.Subproblem 1
x + -6.333333335 = 8.252945603 Simplifying x + -6.333333335 = 8.252945603 Reorder the terms: -6.333333335 + x = 8.252945603 Solving -6.333333335 + x = 8.252945603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = 8.252945603 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 8.252945603 + 6.333333335 x = 8.252945603 + 6.333333335 Combine like terms: 8.252945603 + 6.333333335 = 14.586278938 x = 14.586278938 Simplifying x = 14.586278938Subproblem 2
x + -6.333333335 = -8.252945603 Simplifying x + -6.333333335 = -8.252945603 Reorder the terms: -6.333333335 + x = -8.252945603 Solving -6.333333335 + x = -8.252945603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = -8.252945603 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -8.252945603 + 6.333333335 x = -8.252945603 + 6.333333335 Combine like terms: -8.252945603 + 6.333333335 = -1.919612268 x = -1.919612268 Simplifying x = -1.919612268Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.586278938, -1.919612268}
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