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Simplifying 9x2 + -6x + 14 = -7 Reorder the terms: 14 + -6x + 9x2 = -7 Solving 14 + -6x + 9x2 = -7 Solving for variable 'x'. Reorder the terms: 14 + 7 + -6x + 9x2 = -7 + 7 Combine like terms: 14 + 7 = 21 21 + -6x + 9x2 = -7 + 7 Combine like terms: -7 + 7 = 0 21 + -6x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -2x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -2x + 3x2 = 0 Solving 7 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -0.6666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -0.6666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + -2.333333333 -0.6666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -0.6666666667x + x2 = -2.333333333 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -2.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -2.333333333 + 0.1111111112 Combine like terms: -2.333333333 + 0.1111111112 = -2.2222222218 0.1111111112 + -0.6666666667x + x2 = -2.2222222218 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -2.2222222218 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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