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Simplifying 0 = 3x2 + 10x + 15 Reorder the terms: 0 = 15 + 10x + 3x2 Solving 0 = 15 + 10x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -10x + -3x2 = 15 + 10x + 3x2 + -15 + -10x + -3x2 Reorder the terms: -15 + -10x + -3x2 = 15 + -15 + 10x + -10x + 3x2 + -3x2 Combine like terms: 15 + -15 = 0 -15 + -10x + -3x2 = 0 + 10x + -10x + 3x2 + -3x2 -15 + -10x + -3x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 -15 + -10x + -3x2 = 0 + 3x2 + -3x2 -15 + -10x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -15 + -10x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 10x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying 15 + 10x + 3x2 = 0 Solving 15 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 3.333333333x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 3.333333333x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3.333333333x + x2 = 0 + -5 3.333333333x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 3.333333333x + x2 = -5 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -5 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -5 + 2.777777779 Combine like terms: -5 + 2.777777779 = -2.222222221 2.777777779 + 3.333333333x + x2 = -2.222222221 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = -2.222222221 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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