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Simplifying 24x2 + -34x = 12 Reorder the terms: -34x + 24x2 = 12 Solving -34x + 24x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -34x + 24x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -34x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -17x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -17x + 12x2)' equal to zero and attempt to solve: Simplifying -6 + -17x + 12x2 = 0 Solving -6 + -17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.416666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.416666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.416666667x + x2 = 0 + 0.5 -1.416666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.416666667x + x2 = 0.5 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = 0.5 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = 0.5 + 0.5017361113 Combine like terms: 0.5 + 0.5017361113 = 1.0017361113 0.5017361113 + -1.416666667x + x2 = 1.0017361113 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 1.0017361113 Calculate the square root of the right side: 1.000867679 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 1.000867679 and -1.000867679.Subproblem 1
x + -0.7083333335 = 1.000867679 Simplifying x + -0.7083333335 = 1.000867679 Reorder the terms: -0.7083333335 + x = 1.000867679 Solving -0.7083333335 + x = 1.000867679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = 1.000867679 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 1.000867679 + 0.7083333335 x = 1.000867679 + 0.7083333335 Combine like terms: 1.000867679 + 0.7083333335 = 1.7092010125 x = 1.7092010125 Simplifying x = 1.7092010125Subproblem 2
x + -0.7083333335 = -1.000867679 Simplifying x + -0.7083333335 = -1.000867679 Reorder the terms: -0.7083333335 + x = -1.000867679 Solving -0.7083333335 + x = -1.000867679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = -1.000867679 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -1.000867679 + 0.7083333335 x = -1.000867679 + 0.7083333335 Combine like terms: -1.000867679 + 0.7083333335 = -0.2925343455 x = -0.2925343455 Simplifying x = -0.2925343455Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7092010125, -0.2925343455}Solution
x = {1.7092010125, -0.2925343455}
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