30v^2-66v-45=0

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Solution for 30v^2-66v-45=0 equation:


Simplifying
30v2 + -66v + -45 = 0

Reorder the terms:
-45 + -66v + 30v2 = 0

Solving
-45 + -66v + 30v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -22v + 10v2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-15 + -22v + 10v2)' equal to zero and attempt to solve: Simplifying -15 + -22v + 10v2 = 0 Solving -15 + -22v + 10v2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -2.2v + v2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.2v + 1.5 + v2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.2v + v2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.2v + v2 = 0.0 + 1.5 -2.2v + v2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -2.2v + v2 = 1.5 The v term is -2.2v. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2v + 1.21 + v2 = 1.5 + 1.21 Reorder the terms: 1.21 + -2.2v + v2 = 1.5 + 1.21 Combine like terms: 1.5 + 1.21 = 2.71 1.21 + -2.2v + v2 = 2.71 Factor a perfect square on the left side: (v + -1.1)(v + -1.1) = 2.71 Calculate the square root of the right side: 1.646207763 Break this problem into two subproblems by setting (v + -1.1) equal to 1.646207763 and -1.646207763.

Subproblem 1

v + -1.1 = 1.646207763 Simplifying v + -1.1 = 1.646207763 Reorder the terms: -1.1 + v = 1.646207763 Solving -1.1 + v = 1.646207763 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + v = 1.646207763 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = 1.646207763 + 1.1 v = 1.646207763 + 1.1 Combine like terms: 1.646207763 + 1.1 = 2.746207763 v = 2.746207763 Simplifying v = 2.746207763

Subproblem 2

v + -1.1 = -1.646207763 Simplifying v + -1.1 = -1.646207763 Reorder the terms: -1.1 + v = -1.646207763 Solving -1.1 + v = -1.646207763 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + v = -1.646207763 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = -1.646207763 + 1.1 v = -1.646207763 + 1.1 Combine like terms: -1.646207763 + 1.1 = -0.546207763 v = -0.546207763 Simplifying v = -0.546207763

Solution

The solution to the problem is based on the solutions from the subproblems. v = {2.746207763, -0.546207763}

Solution

v = {2.746207763, -0.546207763}

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