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Simplifying 21x2 + 15x + 18 = 0 Reorder the terms: 18 + 15x + 21x2 = 0 Solving 18 + 15x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 5x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 7x2 = 0 Solving 6 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 0.7142857143x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 0.7142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + -0.8571428571 0.7142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 0.7142857143x + x2 = -0.8571428571 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -0.8571428571 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -0.8571428571 + 0.1275510204 Combine like terms: -0.8571428571 + 0.1275510204 = -0.7295918367 0.1275510204 + 0.7142857143x + x2 = -0.7295918367 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = -0.7295918367 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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