7-8z^2=6z+16

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Solution for 7-8z^2=6z+16 equation:


Simplifying
7 + -8z2 = 6z + 16

Reorder the terms:
7 + -8z2 = 16 + 6z

Solving
7 + -8z2 = 16 + 6z

Solving for variable 'z'.

Reorder the terms:
7 + -16 + -6z + -8z2 = 16 + 6z + -16 + -6z

Combine like terms: 7 + -16 = -9
-9 + -6z + -8z2 = 16 + 6z + -16 + -6z

Reorder the terms:
-9 + -6z + -8z2 = 16 + -16 + 6z + -6z

Combine like terms: 16 + -16 = 0
-9 + -6z + -8z2 = 0 + 6z + -6z
-9 + -6z + -8z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-9 + -6z + -8z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 6z + 8z2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(9 + 6z + 8z2)' equal to zero and attempt to solve: Simplifying 9 + 6z + 8z2 = 0 Solving 9 + 6z + 8z2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 0.75z + z2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 0.75z + -1.125 + z2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 0.75z + z2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 0.75z + z2 = 0 + -1.125 0.75z + z2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 0.75z + z2 = -1.125 The z term is 0.75z. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75z + 0.140625 + z2 = -1.125 + 0.140625 Reorder the terms: 0.140625 + 0.75z + z2 = -1.125 + 0.140625 Combine like terms: -1.125 + 0.140625 = -0.984375 0.140625 + 0.75z + z2 = -0.984375 Factor a perfect square on the left side: (z + 0.375)(z + 0.375) = -0.984375 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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