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Simplifying -5v2 + 36v + 49 = 0 Reorder the terms: 49 + 36v + -5v2 = 0 Solving 49 + 36v + -5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9.8 + -7.2v + v2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + -7.2v + 9.8 + v2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + -7.2v + v2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + -7.2v + v2 = 0 + 9.8 -7.2v + v2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 -7.2v + v2 = 9.8 The v term is -7.2v. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2v + 12.96 + v2 = 9.8 + 12.96 Reorder the terms: 12.96 + -7.2v + v2 = 9.8 + 12.96 Combine like terms: 9.8 + 12.96 = 22.76 12.96 + -7.2v + v2 = 22.76 Factor a perfect square on the left side: (v + -3.6)(v + -3.6) = 22.76 Calculate the square root of the right side: 4.770744177 Break this problem into two subproblems by setting (v + -3.6) equal to 4.770744177 and -4.770744177.Subproblem 1
v + -3.6 = 4.770744177 Simplifying v + -3.6 = 4.770744177 Reorder the terms: -3.6 + v = 4.770744177 Solving -3.6 + v = 4.770744177 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + v = 4.770744177 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + v = 4.770744177 + 3.6 v = 4.770744177 + 3.6 Combine like terms: 4.770744177 + 3.6 = 8.370744177 v = 8.370744177 Simplifying v = 8.370744177Subproblem 2
v + -3.6 = -4.770744177 Simplifying v + -3.6 = -4.770744177 Reorder the terms: -3.6 + v = -4.770744177 Solving -3.6 + v = -4.770744177 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + v = -4.770744177 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + v = -4.770744177 + 3.6 v = -4.770744177 + 3.6 Combine like terms: -4.770744177 + 3.6 = -1.170744177 v = -1.170744177 Simplifying v = -1.170744177Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.370744177, -1.170744177}
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