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Simplifying 21x = 18x2 + 15 Reorder the terms: 21x = 15 + 18x2 Solving 21x = 15 + 18x2 Solving for variable 'x'. Reorder the terms: -15 + 21x + -18x2 = 15 + 18x2 + -15 + -18x2 Reorder the terms: -15 + 21x + -18x2 = 15 + -15 + 18x2 + -18x2 Combine like terms: 15 + -15 = 0 -15 + 21x + -18x2 = 0 + 18x2 + -18x2 -15 + 21x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -15 + 21x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 7x + -6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 7x + -6x2)' equal to zero and attempt to solve: Simplifying -5 + 7x + -6x2 = 0 Solving -5 + 7x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.8333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -1.166666667x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -1.166666667x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + -0.8333333333 -1.166666667x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -1.166666667x + x2 = -0.8333333333 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = -0.8333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -0.8333333333 + 0.3402777780 Combine like terms: -0.8333333333 + 0.3402777780 = -0.4930555553 0.3402777780 + -1.166666667x + x2 = -0.4930555553 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = -0.4930555553 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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