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Simplifying 2v2 + -10v + 13 = (v + 1)(v + 1) Reorder the terms: 13 + -10v + 2v2 = (v + 1)(v + 1) Reorder the terms: 13 + -10v + 2v2 = (1 + v)(v + 1) Reorder the terms: 13 + -10v + 2v2 = (1 + v)(1 + v) Multiply (1 + v) * (1 + v) 13 + -10v + 2v2 = (1(1 + v) + v(1 + v)) 13 + -10v + 2v2 = ((1 * 1 + v * 1) + v(1 + v)) 13 + -10v + 2v2 = ((1 + 1v) + v(1 + v)) 13 + -10v + 2v2 = (1 + 1v + (1 * v + v * v)) 13 + -10v + 2v2 = (1 + 1v + (1v + v2)) Combine like terms: 1v + 1v = 2v 13 + -10v + 2v2 = (1 + 2v + v2) Solving 13 + -10v + 2v2 = 1 + 2v + v2 Solving for variable 'v'. Reorder the terms: 13 + -1 + -10v + -2v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2 Combine like terms: 13 + -1 = 12 12 + -10v + -2v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2 Combine like terms: -10v + -2v = -12v 12 + -12v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 12 + -12v + 1v2 = 1 + 2v + v2 + -1 + -2v + -1v2 Reorder the terms: 12 + -12v + 1v2 = 1 + -1 + 2v + -2v + v2 + -1v2 Combine like terms: 1 + -1 = 0 12 + -12v + 1v2 = 0 + 2v + -2v + v2 + -1v2 12 + -12v + 1v2 = 2v + -2v + v2 + -1v2 Combine like terms: 2v + -2v = 0 12 + -12v + 1v2 = 0 + v2 + -1v2 12 + -12v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 12 + -12v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -12v + -12 + v2 = 0 + -12 Reorder the terms: 12 + -12 + -12v + v2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12v + v2 = 0 + -12 -12v + v2 = 0 + -12 Combine like terms: 0 + -12 = -12 -12v + v2 = -12 The v term is -12v. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12v + 36 + v2 = -12 + 36 Reorder the terms: 36 + -12v + v2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + -12v + v2 = 24 Factor a perfect square on the left side: (v + -6)(v + -6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (v + -6) equal to 4.898979486 and -4.898979486.Subproblem 1
v + -6 = 4.898979486 Simplifying v + -6 = 4.898979486 Reorder the terms: -6 + v = 4.898979486 Solving -6 + v = 4.898979486 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + v = 4.898979486 + 6 v = 4.898979486 + 6 Combine like terms: 4.898979486 + 6 = 10.898979486 v = 10.898979486 Simplifying v = 10.898979486Subproblem 2
v + -6 = -4.898979486 Simplifying v + -6 = -4.898979486 Reorder the terms: -6 + v = -4.898979486 Solving -6 + v = -4.898979486 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = -4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + v = -4.898979486 + 6 v = -4.898979486 + 6 Combine like terms: -4.898979486 + 6 = 1.101020514 v = 1.101020514 Simplifying v = 1.101020514Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.898979486, 1.101020514}
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