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Simplifying 24x2 + 274x + -84 = 0 Reorder the terms: -84 + 274x + 24x2 = 0 Solving -84 + 274x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 137x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 137x + 12x2)' equal to zero and attempt to solve: Simplifying -42 + 137x + 12x2 = 0 Solving -42 + 137x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.5 + 11.41666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 11.41666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 11.41666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 11.41666667x + x2 = 0 + 3.5 11.41666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 11.41666667x + x2 = 3.5 The x term is 11.41666667x. Take half its coefficient (5.708333335). Square it (32.58506946) and add it to both sides. Add '32.58506946' to each side of the equation. 11.41666667x + 32.58506946 + x2 = 3.5 + 32.58506946 Reorder the terms: 32.58506946 + 11.41666667x + x2 = 3.5 + 32.58506946 Combine like terms: 3.5 + 32.58506946 = 36.08506946 32.58506946 + 11.41666667x + x2 = 36.08506946 Factor a perfect square on the left side: (x + 5.708333335)(x + 5.708333335) = 36.08506946 Calculate the square root of the right side: 6.007084939 Break this problem into two subproblems by setting (x + 5.708333335) equal to 6.007084939 and -6.007084939.Subproblem 1
x + 5.708333335 = 6.007084939 Simplifying x + 5.708333335 = 6.007084939 Reorder the terms: 5.708333335 + x = 6.007084939 Solving 5.708333335 + x = 6.007084939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.708333335' to each side of the equation. 5.708333335 + -5.708333335 + x = 6.007084939 + -5.708333335 Combine like terms: 5.708333335 + -5.708333335 = 0.000000000 0.000000000 + x = 6.007084939 + -5.708333335 x = 6.007084939 + -5.708333335 Combine like terms: 6.007084939 + -5.708333335 = 0.298751604 x = 0.298751604 Simplifying x = 0.298751604Subproblem 2
x + 5.708333335 = -6.007084939 Simplifying x + 5.708333335 = -6.007084939 Reorder the terms: 5.708333335 + x = -6.007084939 Solving 5.708333335 + x = -6.007084939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.708333335' to each side of the equation. 5.708333335 + -5.708333335 + x = -6.007084939 + -5.708333335 Combine like terms: 5.708333335 + -5.708333335 = 0.000000000 0.000000000 + x = -6.007084939 + -5.708333335 x = -6.007084939 + -5.708333335 Combine like terms: -6.007084939 + -5.708333335 = -11.715418274 x = -11.715418274 Simplifying x = -11.715418274Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.298751604, -11.715418274}Solution
x = {0.298751604, -11.715418274}
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