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Simplifying -7v(v + -6) = -38 Reorder the terms: -7v(-6 + v) = -38 (-6 * -7v + v * -7v) = -38 (42v + -7v2) = -38 Solving 42v + -7v2 = -38 Solving for variable 'v'. Reorder the terms: 38 + 42v + -7v2 = -38 + 38 Combine like terms: -38 + 38 = 0 38 + 42v + -7v2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -5.428571429 + -6v + v2 = 0 Move the constant term to the right: Add '5.428571429' to each side of the equation. -5.428571429 + -6v + 5.428571429 + v2 = 0 + 5.428571429 Reorder the terms: -5.428571429 + 5.428571429 + -6v + v2 = 0 + 5.428571429 Combine like terms: -5.428571429 + 5.428571429 = 0.000000000 0.000000000 + -6v + v2 = 0 + 5.428571429 -6v + v2 = 0 + 5.428571429 Combine like terms: 0 + 5.428571429 = 5.428571429 -6v + v2 = 5.428571429 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = 5.428571429 + 9 Reorder the terms: 9 + -6v + v2 = 5.428571429 + 9 Combine like terms: 5.428571429 + 9 = 14.428571429 9 + -6v + v2 = 14.428571429 Factor a perfect square on the left side: (v + -3)(v + -3) = 14.428571429 Calculate the square root of the right side: 3.798495943 Break this problem into two subproblems by setting (v + -3) equal to 3.798495943 and -3.798495943.Subproblem 1
v + -3 = 3.798495943 Simplifying v + -3 = 3.798495943 Reorder the terms: -3 + v = 3.798495943 Solving -3 + v = 3.798495943 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 3.798495943 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.798495943 + 3 v = 3.798495943 + 3 Combine like terms: 3.798495943 + 3 = 6.798495943 v = 6.798495943 Simplifying v = 6.798495943Subproblem 2
v + -3 = -3.798495943 Simplifying v + -3 = -3.798495943 Reorder the terms: -3 + v = -3.798495943 Solving -3 + v = -3.798495943 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -3.798495943 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.798495943 + 3 v = -3.798495943 + 3 Combine like terms: -3.798495943 + 3 = -0.798495943 v = -0.798495943 Simplifying v = -0.798495943Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.798495943, -0.798495943}
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