v^2-18v+24=4

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Solution for v^2-18v+24=4 equation:


Simplifying
v2 + -18v + 24 = 4

Reorder the terms:
24 + -18v + v2 = 4

Solving
24 + -18v + v2 = 4

Solving for variable 'v'.

Reorder the terms:
24 + -4 + -18v + v2 = 4 + -4

Combine like terms: 24 + -4 = 20
20 + -18v + v2 = 4 + -4

Combine like terms: 4 + -4 = 0
20 + -18v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -18v + -20 + v2 = 0 + -20

Reorder the terms:
20 + -20 + -18v + v2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -18v + v2 = 0 + -20
-18v + v2 = 0 + -20

Combine like terms: 0 + -20 = -20
-18v + v2 = -20

The v term is -18v.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18v + 81 + v2 = -20 + 81

Reorder the terms:
81 + -18v + v2 = -20 + 81

Combine like terms: -20 + 81 = 61
81 + -18v + v2 = 61

Factor a perfect square on the left side:
(v + -9)(v + -9) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(v + -9) equal to 7.810249676 and -7.810249676.

Subproblem 1

v + -9 = 7.810249676 Simplifying v + -9 = 7.810249676 Reorder the terms: -9 + v = 7.810249676 Solving -9 + v = 7.810249676 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = 7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + v = 7.810249676 + 9 v = 7.810249676 + 9 Combine like terms: 7.810249676 + 9 = 16.810249676 v = 16.810249676 Simplifying v = 16.810249676

Subproblem 2

v + -9 = -7.810249676 Simplifying v + -9 = -7.810249676 Reorder the terms: -9 + v = -7.810249676 Solving -9 + v = -7.810249676 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = -7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + v = -7.810249676 + 9 v = -7.810249676 + 9 Combine like terms: -7.810249676 + 9 = 1.189750324 v = 1.189750324 Simplifying v = 1.189750324

Solution

The solution to the problem is based on the solutions from the subproblems. v = {16.810249676, 1.189750324}

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