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Simplifying 0 = v2 + 7v + -10 Reorder the terms: 0 = -10 + 7v + v2 Solving 0 = -10 + 7v + v2 Solving for variable 'v'. Combine like terms: 0 + 10 = 10 10 + -7v + -1v2 = -10 + 7v + v2 + 10 + -7v + -1v2 Reorder the terms: 10 + -7v + -1v2 = -10 + 10 + 7v + -7v + v2 + -1v2 Combine like terms: -10 + 10 = 0 10 + -7v + -1v2 = 0 + 7v + -7v + v2 + -1v2 10 + -7v + -1v2 = 7v + -7v + v2 + -1v2 Combine like terms: 7v + -7v = 0 10 + -7v + -1v2 = 0 + v2 + -1v2 10 + -7v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 10 + -7v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 7v + v2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 7v + 10 + v2 = 0 + 10 Reorder the terms: -10 + 10 + 7v + v2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7v + v2 = 0 + 10 7v + v2 = 0 + 10 Combine like terms: 0 + 10 = 10 7v + v2 = 10 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 = 10 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + 7v + v2 = 22.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (v + 3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
v + 3.5 = 4.716990566 Simplifying v + 3.5 = 4.716990566 Reorder the terms: 3.5 + v = 4.716990566 Solving 3.5 + v = 4.716990566 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 = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 4.716990566 + -3.5 v = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 v = 1.216990566 Simplifying v = 1.216990566Subproblem 2
v + 3.5 = -4.716990566 Simplifying v + 3.5 = -4.716990566 Reorder the terms: 3.5 + v = -4.716990566 Solving 3.5 + v = -4.716990566 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 = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -4.716990566 + -3.5 v = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 v = -8.216990566 Simplifying v = -8.216990566Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.216990566, -8.216990566}
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