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Simplifying 16x2 + -30x + -24 = 0 Reorder the terms: -24 + -30x + 16x2 = 0 Solving -24 + -30x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying -12 + -15x + 8x2 = 0 Solving -12 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.5 + -1.875x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.875x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.875x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.875x + x2 = 0 + 1.5 -1.875x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.875x + x2 = 1.5 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 1.5 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 1.5 + 0.87890625 Combine like terms: 1.5 + 0.87890625 = 2.37890625 0.87890625 + -1.875x + x2 = 2.37890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 2.37890625 Calculate the square root of the right side: 1.542370335 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.542370335 and -1.542370335.Subproblem 1
x + -0.9375 = 1.542370335 Simplifying x + -0.9375 = 1.542370335 Reorder the terms: -0.9375 + x = 1.542370335 Solving -0.9375 + x = 1.542370335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.542370335 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.542370335 + 0.9375 x = 1.542370335 + 0.9375 Combine like terms: 1.542370335 + 0.9375 = 2.479870335 x = 2.479870335 Simplifying x = 2.479870335Subproblem 2
x + -0.9375 = -1.542370335 Simplifying x + -0.9375 = -1.542370335 Reorder the terms: -0.9375 + x = -1.542370335 Solving -0.9375 + x = -1.542370335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.542370335 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.542370335 + 0.9375 x = -1.542370335 + 0.9375 Combine like terms: -1.542370335 + 0.9375 = -0.604870335 x = -0.604870335 Simplifying x = -0.604870335Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.479870335, -0.604870335}Solution
x = {2.479870335, -0.604870335}
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