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Simplifying 18x2 + 48x + 38 = 0 Reorder the terms: 38 + 48x + 18x2 = 0 Solving 38 + 48x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 24x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 24x + 9x2)' equal to zero and attempt to solve: Simplifying 19 + 24x + 9x2 = 0 Solving 19 + 24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.111111111 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-2.111111111' to each side of the equation. 2.111111111 + 2.666666667x + -2.111111111 + x2 = 0 + -2.111111111 Reorder the terms: 2.111111111 + -2.111111111 + 2.666666667x + x2 = 0 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + -2.111111111 2.666666667x + x2 = 0 + -2.111111111 Combine like terms: 0 + -2.111111111 = -2.111111111 2.666666667x + x2 = -2.111111111 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -2.111111111 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -2.111111111 + 1.777777780 Combine like terms: -2.111111111 + 1.777777780 = -0.333333331 1.777777780 + 2.666666667x + x2 = -0.333333331 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -0.333333331 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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