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Simplifying 3v2 + -5v = 9 Reorder the terms: -5v + 3v2 = 9 Solving -5v + 3v2 = 9 Solving for variable 'v'. Reorder the terms: -9 + -5v + 3v2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -5v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -1.666666667v + v2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.666666667v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -1.666666667v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.666666667v + v2 = 0 + 3 -1.666666667v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.666666667v + v2 = 3 The v term is -1.666666667v. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667v + 0.6944444447 + v2 = 3 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667v + v2 = 3 + 0.6944444447 Combine like terms: 3 + 0.6944444447 = 3.6944444447 0.6944444447 + -1.666666667v + v2 = 3.6944444447 Factor a perfect square on the left side: (v + -0.8333333335)(v + -0.8333333335) = 3.6944444447 Calculate the square root of the right side: 1.922093766 Break this problem into two subproblems by setting (v + -0.8333333335) equal to 1.922093766 and -1.922093766.Subproblem 1
v + -0.8333333335 = 1.922093766 Simplifying v + -0.8333333335 = 1.922093766 Reorder the terms: -0.8333333335 + v = 1.922093766 Solving -0.8333333335 + v = 1.922093766 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + v = 1.922093766 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + v = 1.922093766 + 0.8333333335 v = 1.922093766 + 0.8333333335 Combine like terms: 1.922093766 + 0.8333333335 = 2.7554270995 v = 2.7554270995 Simplifying v = 2.7554270995Subproblem 2
v + -0.8333333335 = -1.922093766 Simplifying v + -0.8333333335 = -1.922093766 Reorder the terms: -0.8333333335 + v = -1.922093766 Solving -0.8333333335 + v = -1.922093766 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + v = -1.922093766 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + v = -1.922093766 + 0.8333333335 v = -1.922093766 + 0.8333333335 Combine like terms: -1.922093766 + 0.8333333335 = -1.0887604325 v = -1.0887604325 Simplifying v = -1.0887604325Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.7554270995, -1.0887604325}
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