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Simplifying v(3v + -17) = 21 Reorder the terms: v(-17 + 3v) = 21 (-17 * v + 3v * v) = 21 (-17v + 3v2) = 21 Solving -17v + 3v2 = 21 Solving for variable 'v'. Reorder the terms: -21 + -17v + 3v2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -17v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + -5.666666667v + v2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.666666667v + 7 + v2 = 0 + 7 Reorder the terms: -7 + 7 + -5.666666667v + v2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.666666667v + v2 = 0 + 7 -5.666666667v + v2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.666666667v + v2 = 7 The v term is -5.666666667v. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667v + 8.027777782 + v2 = 7 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667v + v2 = 7 + 8.027777782 Combine like terms: 7 + 8.027777782 = 15.027777782 8.027777782 + -5.666666667v + v2 = 15.027777782 Factor a perfect square on the left side: (v + -2.833333334)(v + -2.833333334) = 15.027777782 Calculate the square root of the right side: 3.876567784 Break this problem into two subproblems by setting (v + -2.833333334) equal to 3.876567784 and -3.876567784.Subproblem 1
v + -2.833333334 = 3.876567784 Simplifying v + -2.833333334 = 3.876567784 Reorder the terms: -2.833333334 + v = 3.876567784 Solving -2.833333334 + v = 3.876567784 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + v = 3.876567784 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + v = 3.876567784 + 2.833333334 v = 3.876567784 + 2.833333334 Combine like terms: 3.876567784 + 2.833333334 = 6.709901118 v = 6.709901118 Simplifying v = 6.709901118Subproblem 2
v + -2.833333334 = -3.876567784 Simplifying v + -2.833333334 = -3.876567784 Reorder the terms: -2.833333334 + v = -3.876567784 Solving -2.833333334 + v = -3.876567784 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + v = -3.876567784 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + v = -3.876567784 + 2.833333334 v = -3.876567784 + 2.833333334 Combine like terms: -3.876567784 + 2.833333334 = -1.04323445 v = -1.04323445 Simplifying v = -1.04323445Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.709901118, -1.04323445}
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