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Simplifying 28 = -4n(n + 15) Reorder the terms: 28 = -4n(15 + n) 28 = (15 * -4n + n * -4n) 28 = (-60n + -4n2) Solving 28 = -60n + -4n2 Solving for variable 'n'. Reorder the terms: 28 + 60n + 4n2 = -60n + 60n + -4n2 + 4n2 Combine like terms: -60n + 60n = 0 28 + 60n + 4n2 = 0 + -4n2 + 4n2 28 + 60n + 4n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 28 + 60n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + 15n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + 15n + n2)' equal to zero and attempt to solve: Simplifying 7 + 15n + n2 = 0 Solving 7 + 15n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 15n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + 15n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 15n + n2 = 0 + -7 15n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 15n + n2 = -7 The n term is 15n. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15n + 56.25 + n2 = -7 + 56.25 Reorder the terms: 56.25 + 15n + n2 = -7 + 56.25 Combine like terms: -7 + 56.25 = 49.25 56.25 + 15n + n2 = 49.25 Factor a perfect square on the left side: (n + 7.5)(n + 7.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (n + 7.5) equal to 7.017834424 and -7.017834424.Subproblem 1
n + 7.5 = 7.017834424 Simplifying n + 7.5 = 7.017834424 Reorder the terms: 7.5 + n = 7.017834424 Solving 7.5 + n = 7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + n = 7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + n = 7.017834424 + -7.5 n = 7.017834424 + -7.5 Combine like terms: 7.017834424 + -7.5 = -0.482165576 n = -0.482165576 Simplifying n = -0.482165576Subproblem 2
n + 7.5 = -7.017834424 Simplifying n + 7.5 = -7.017834424 Reorder the terms: 7.5 + n = -7.017834424 Solving 7.5 + n = -7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + n = -7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + n = -7.017834424 + -7.5 n = -7.017834424 + -7.5 Combine like terms: -7.017834424 + -7.5 = -14.517834424 n = -14.517834424 Simplifying n = -14.517834424Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.482165576, -14.517834424}Solution
n = {-0.482165576, -14.517834424}
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