5z^2-7z=-3z-7

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Solution for 5z^2-7z=-3z-7 equation: 


Simplifying
5z2 + -7z = -3z + -7

Reorder the terms:
-7z + 5z2 = -3z + -7

Reorder the terms:
-7z + 5z2 = -7 + -3z

Solving
-7z + 5z2 = -7 + -3z

Solving for variable 'z'.

Reorder the terms:
7 + -7z + 3z + 5z2 = -7 + -3z + 7 + 3z

Combine like terms: -7z + 3z = -4z
7 + -4z + 5z2 = -7 + -3z + 7 + 3z

Reorder the terms:
7 + -4z + 5z2 = -7 + 7 + -3z + 3z

Combine like terms: -7 + 7 = 0
7 + -4z + 5z2 = 0 + -3z + 3z
7 + -4z + 5z2 = -3z + 3z

Combine like terms: -3z + 3z = 0
7 + -4z + 5z2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.4 + -0.8z + z2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -0.8z + -1.4 + z2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -0.8z + z2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -0.8z + z2 = 0 + -1.4
-0.8z + z2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-0.8z + z2 = -1.4

The z term is -0.8z.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8z + 0.16 + z2 = -1.4 + 0.16

Reorder the terms:
0.16 + -0.8z + z2 = -1.4 + 0.16

Combine like terms: -1.4 + 0.16 = -1.24
0.16 + -0.8z + z2 = -1.24

Factor a perfect square on the left side:
(z + -0.4)(z + -0.4) = -1.24

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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