7v^2-49v=84

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Solution for 7v^2-49v=84 equation:


Simplifying
7v2 + -49v = 84

Reorder the terms:
-49v + 7v2 = 84

Solving
-49v + 7v2 = 84

Solving for variable 'v'.

Reorder the terms:
-84 + -49v + 7v2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -49v + 7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + -7v + v2) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-12 + -7v + v2)' equal to zero and attempt to solve: Simplifying -12 + -7v + v2 = 0 Solving -12 + -7v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -7v + 12 + v2 = 0 + 12 Reorder the terms: -12 + 12 + -7v + v2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -7v + v2 = 0 + 12 -7v + v2 = 0 + 12 Combine like terms: 0 + 12 = 12 -7v + v2 = 12 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = 12 + 12.25 Reorder the terms: 12.25 + -7v + v2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + -7v + v2 = 24.25 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (v + -3.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

v + -3.5 = 4.924428901 Simplifying v + -3.5 = 4.924428901 Reorder the terms: -3.5 + v = 4.924428901 Solving -3.5 + v = 4.924428901 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 4.924428901 + 3.5 v = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 v = 8.424428901 Simplifying v = 8.424428901

Subproblem 2

v + -3.5 = -4.924428901 Simplifying v + -3.5 = -4.924428901 Reorder the terms: -3.5 + v = -4.924428901 Solving -3.5 + v = -4.924428901 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -4.924428901 + 3.5 v = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 v = -1.424428901 Simplifying v = -1.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. v = {8.424428901, -1.424428901}

Solution

v = {8.424428901, -1.424428901}

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