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Simplifying 9v2 + -2v + -15 = 0 Reorder the terms: -15 + -2v + 9v2 = 0 Solving -15 + -2v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + -0.2222222222v + v2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.2222222222v + 1.666666667 + v2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.2222222222v + v2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.2222222222v + v2 = 0 + 1.666666667 -0.2222222222v + v2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.2222222222v + v2 = 1.666666667 The v term is -0.2222222222v. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222v + 0.01234567901 + v2 = 1.666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222v + v2 = 1.666666667 + 0.01234567901 Combine like terms: 1.666666667 + 0.01234567901 = 1.67901234601 0.01234567901 + -0.2222222222v + v2 = 1.67901234601 Factor a perfect square on the left side: (v + -0.1111111111)(v + -0.1111111111) = 1.67901234601 Calculate the square root of the right side: 1.295767088 Break this problem into two subproblems by setting (v + -0.1111111111) equal to 1.295767088 and -1.295767088.Subproblem 1
v + -0.1111111111 = 1.295767088 Simplifying v + -0.1111111111 = 1.295767088 Reorder the terms: -0.1111111111 + v = 1.295767088 Solving -0.1111111111 + v = 1.295767088 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + v = 1.295767088 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + v = 1.295767088 + 0.1111111111 v = 1.295767088 + 0.1111111111 Combine like terms: 1.295767088 + 0.1111111111 = 1.4068781991 v = 1.4068781991 Simplifying v = 1.4068781991Subproblem 2
v + -0.1111111111 = -1.295767088 Simplifying v + -0.1111111111 = -1.295767088 Reorder the terms: -0.1111111111 + v = -1.295767088 Solving -0.1111111111 + v = -1.295767088 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + v = -1.295767088 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + v = -1.295767088 + 0.1111111111 v = -1.295767088 + 0.1111111111 Combine like terms: -1.295767088 + 0.1111111111 = -1.1846559769 v = -1.1846559769 Simplifying v = -1.1846559769Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.4068781991, -1.1846559769}
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