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Simplifying 48x2 + -18x + -4 = 0 Reorder the terms: -4 + -18x + 48x2 = 0 Solving -4 + -18x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -9x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -9x + 24x2)' equal to zero and attempt to solve: Simplifying -2 + -9x + 24x2 = 0 Solving -2 + -9x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.08333333333 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -0.375x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -0.375x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -0.375x + x2 = 0 + 0.08333333333 -0.375x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -0.375x + x2 = 0.08333333333 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.08333333333 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.08333333333 + 0.03515625 Combine like terms: 0.08333333333 + 0.03515625 = 0.11848958333 0.03515625 + -0.375x + x2 = 0.11848958333 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.11848958333 Calculate the square root of the right side: 0.344223159 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.344223159 and -0.344223159.Subproblem 1
x + -0.1875 = 0.344223159 Simplifying x + -0.1875 = 0.344223159 Reorder the terms: -0.1875 + x = 0.344223159 Solving -0.1875 + x = 0.344223159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.344223159 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.344223159 + 0.1875 x = 0.344223159 + 0.1875 Combine like terms: 0.344223159 + 0.1875 = 0.531723159 x = 0.531723159 Simplifying x = 0.531723159Subproblem 2
x + -0.1875 = -0.344223159 Simplifying x + -0.1875 = -0.344223159 Reorder the terms: -0.1875 + x = -0.344223159 Solving -0.1875 + x = -0.344223159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.344223159 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.344223159 + 0.1875 x = -0.344223159 + 0.1875 Combine like terms: -0.344223159 + 0.1875 = -0.156723159 x = -0.156723159 Simplifying x = -0.156723159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531723159, -0.156723159}Solution
x = {0.531723159, -0.156723159}
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