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Simplifying 24x2 + 34x + -100 = 0 Reorder the terms: -100 + 34x + 24x2 = 0 Solving -100 + 34x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 17x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 17x + 12x2)' equal to zero and attempt to solve: Simplifying -50 + 17x + 12x2 = 0 Solving -50 + 17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.166666667 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 1.416666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 1.416666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 1.416666667x + x2 = 0 + 4.166666667 1.416666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 1.416666667x + x2 = 4.166666667 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 = 4.166666667 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 4.166666667 + 0.5017361113 Combine like terms: 4.166666667 + 0.5017361113 = 4.6684027783 0.5017361113 + 1.416666667x + x2 = 4.6684027783 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 4.6684027783 Calculate the square root of the right side: 2.160648694 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 2.160648694 and -2.160648694.Subproblem 1
x + 0.7083333335 = 2.160648694 Simplifying x + 0.7083333335 = 2.160648694 Reorder the terms: 0.7083333335 + x = 2.160648694 Solving 0.7083333335 + x = 2.160648694 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 = 2.160648694 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 2.160648694 + -0.7083333335 x = 2.160648694 + -0.7083333335 Combine like terms: 2.160648694 + -0.7083333335 = 1.4523153605 x = 1.4523153605 Simplifying x = 1.4523153605Subproblem 2
x + 0.7083333335 = -2.160648694 Simplifying x + 0.7083333335 = -2.160648694 Reorder the terms: 0.7083333335 + x = -2.160648694 Solving 0.7083333335 + x = -2.160648694 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 = -2.160648694 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -2.160648694 + -0.7083333335 x = -2.160648694 + -0.7083333335 Combine like terms: -2.160648694 + -0.7083333335 = -2.8689820275 x = -2.8689820275 Simplifying x = -2.8689820275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4523153605, -2.8689820275}Solution
x = {1.4523153605, -2.8689820275}
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