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Simplifying 5v2 + -7v + -53 = 0 Reorder the terms: -53 + -7v + 5v2 = 0 Solving -53 + -7v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.6 + -1.4v + v2 = 0 Move the constant term to the right: Add '10.6' to each side of the equation. -10.6 + -1.4v + 10.6 + v2 = 0 + 10.6 Reorder the terms: -10.6 + 10.6 + -1.4v + v2 = 0 + 10.6 Combine like terms: -10.6 + 10.6 = 0.0 0.0 + -1.4v + v2 = 0 + 10.6 -1.4v + v2 = 0 + 10.6 Combine like terms: 0 + 10.6 = 10.6 -1.4v + v2 = 10.6 The v term is -1.4v. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4v + 0.49 + v2 = 10.6 + 0.49 Reorder the terms: 0.49 + -1.4v + v2 = 10.6 + 0.49 Combine like terms: 10.6 + 0.49 = 11.09 0.49 + -1.4v + v2 = 11.09 Factor a perfect square on the left side: (v + -0.7)(v + -0.7) = 11.09 Calculate the square root of the right side: 3.330165161 Break this problem into two subproblems by setting (v + -0.7) equal to 3.330165161 and -3.330165161.Subproblem 1
v + -0.7 = 3.330165161 Simplifying v + -0.7 = 3.330165161 Reorder the terms: -0.7 + v = 3.330165161 Solving -0.7 + v = 3.330165161 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = 3.330165161 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = 3.330165161 + 0.7 v = 3.330165161 + 0.7 Combine like terms: 3.330165161 + 0.7 = 4.030165161 v = 4.030165161 Simplifying v = 4.030165161Subproblem 2
v + -0.7 = -3.330165161 Simplifying v + -0.7 = -3.330165161 Reorder the terms: -0.7 + v = -3.330165161 Solving -0.7 + v = -3.330165161 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = -3.330165161 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = -3.330165161 + 0.7 v = -3.330165161 + 0.7 Combine like terms: -3.330165161 + 0.7 = -2.630165161 v = -2.630165161 Simplifying v = -2.630165161Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.030165161, -2.630165161}
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