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Simplifying 56v2 = 48v + 28 Reorder the terms: 56v2 = 28 + 48v Solving 56v2 = 28 + 48v Solving for variable 'v'. Reorder the terms: -28 + -48v + 56v2 = 28 + 48v + -28 + -48v Reorder the terms: -28 + -48v + 56v2 = 28 + -28 + 48v + -48v Combine like terms: 28 + -28 = 0 -28 + -48v + 56v2 = 0 + 48v + -48v -28 + -48v + 56v2 = 48v + -48v Combine like terms: 48v + -48v = 0 -28 + -48v + 56v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + -12v + 14v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -12v + 14v2)' equal to zero and attempt to solve: Simplifying -7 + -12v + 14v2 = 0 Solving -7 + -12v + 14v2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.5 + -0.8571428571v + v2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.8571428571v + 0.5 + v2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.8571428571v + v2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.8571428571v + v2 = 0 + 0.5 -0.8571428571v + v2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.8571428571v + v2 = 0.5 The v term is -0.8571428571v. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571v + 0.1836734694 + v2 = 0.5 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571v + v2 = 0.5 + 0.1836734694 Combine like terms: 0.5 + 0.1836734694 = 0.6836734694 0.1836734694 + -0.8571428571v + v2 = 0.6836734694 Factor a perfect square on the left side: (v + -0.4285714286)(v + -0.4285714286) = 0.6836734694 Calculate the square root of the right side: 0.826845493 Break this problem into two subproblems by setting (v + -0.4285714286) equal to 0.826845493 and -0.826845493.Subproblem 1
v + -0.4285714286 = 0.826845493 Simplifying v + -0.4285714286 = 0.826845493 Reorder the terms: -0.4285714286 + v = 0.826845493 Solving -0.4285714286 + v = 0.826845493 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = 0.826845493 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = 0.826845493 + 0.4285714286 v = 0.826845493 + 0.4285714286 Combine like terms: 0.826845493 + 0.4285714286 = 1.2554169216 v = 1.2554169216 Simplifying v = 1.2554169216Subproblem 2
v + -0.4285714286 = -0.826845493 Simplifying v + -0.4285714286 = -0.826845493 Reorder the terms: -0.4285714286 + v = -0.826845493 Solving -0.4285714286 + v = -0.826845493 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = -0.826845493 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = -0.826845493 + 0.4285714286 v = -0.826845493 + 0.4285714286 Combine like terms: -0.826845493 + 0.4285714286 = -0.3982740644 v = -0.3982740644 Simplifying v = -0.3982740644Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.2554169216, -0.3982740644}Solution
v = {1.2554169216, -0.3982740644}
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