9z^2-6z+15=0

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Solution for 9z^2-6z+15=0 equation:


Simplifying
9z2 + -6z + 15 = 0

Reorder the terms:
15 + -6z + 9z2 = 0

Solving
15 + -6z + 9z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -2z + 3z2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -2z + 3z2)' equal to zero and attempt to solve: Simplifying 5 + -2z + 3z2 = 0 Solving 5 + -2z + 3z2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -0.6666666667z + z2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -0.6666666667z + -1.666666667 + z2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -0.6666666667z + z2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -0.6666666667z + z2 = 0 + -1.666666667 -0.6666666667z + z2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -0.6666666667z + z2 = -1.666666667 The z term is -0.6666666667z. 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. -0.6666666667z + 0.1111111112 + z2 = -1.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667z + z2 = -1.666666667 + 0.1111111112 Combine like terms: -1.666666667 + 0.1111111112 = -1.5555555558 0.1111111112 + -0.6666666667z + z2 = -1.5555555558 Factor a perfect square on the left side: (z + -0.3333333334)(z + -0.3333333334) = -1.5555555558 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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