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Simplifying 50x2 + -24x + -6 = 0 Reorder the terms: -6 + -24x + 50x2 = 0 Solving -6 + -24x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -12x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -12x + 25x2)' equal to zero and attempt to solve: Simplifying -3 + -12x + 25x2 = 0 Solving -3 + -12x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.12 + -0.48x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.48x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.48x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.48x + x2 = 0 + 0.12 -0.48x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.48x + x2 = 0.12 The x term is -0.48x. Take half its coefficient (-0.24). Square it (0.0576) and add it to both sides. Add '0.0576' to each side of the equation. -0.48x + 0.0576 + x2 = 0.12 + 0.0576 Reorder the terms: 0.0576 + -0.48x + x2 = 0.12 + 0.0576 Combine like terms: 0.12 + 0.0576 = 0.1776 0.0576 + -0.48x + x2 = 0.1776 Factor a perfect square on the left side: (x + -0.24)(x + -0.24) = 0.1776 Calculate the square root of the right side: 0.42142615 Break this problem into two subproblems by setting (x + -0.24) equal to 0.42142615 and -0.42142615.Subproblem 1
x + -0.24 = 0.42142615 Simplifying x + -0.24 = 0.42142615 Reorder the terms: -0.24 + x = 0.42142615 Solving -0.24 + x = 0.42142615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = 0.42142615 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = 0.42142615 + 0.24 x = 0.42142615 + 0.24 Combine like terms: 0.42142615 + 0.24 = 0.66142615 x = 0.66142615 Simplifying x = 0.66142615Subproblem 2
x + -0.24 = -0.42142615 Simplifying x + -0.24 = -0.42142615 Reorder the terms: -0.24 + x = -0.42142615 Solving -0.24 + x = -0.42142615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = -0.42142615 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = -0.42142615 + 0.24 x = -0.42142615 + 0.24 Combine like terms: -0.42142615 + 0.24 = -0.18142615 x = -0.18142615 Simplifying x = -0.18142615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66142615, -0.18142615}Solution
x = {0.66142615, -0.18142615}
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