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Simplifying 6n2 + 16n + -700 = 0 Reorder the terms: -700 + 16n + 6n2 = 0 Solving -700 + 16n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-350 + 8n + 3n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-350 + 8n + 3n2)' equal to zero and attempt to solve: Simplifying -350 + 8n + 3n2 = 0 Solving -350 + 8n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -116.6666667 + 2.666666667n + n2 = 0 Move the constant term to the right: Add '116.6666667' to each side of the equation. -116.6666667 + 2.666666667n + 116.6666667 + n2 = 0 + 116.6666667 Reorder the terms: -116.6666667 + 116.6666667 + 2.666666667n + n2 = 0 + 116.6666667 Combine like terms: -116.6666667 + 116.6666667 = 0.0000000 0.0000000 + 2.666666667n + n2 = 0 + 116.6666667 2.666666667n + n2 = 0 + 116.6666667 Combine like terms: 0 + 116.6666667 = 116.6666667 2.666666667n + n2 = 116.6666667 The n term is 2.666666667n. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667n + 1.777777780 + n2 = 116.6666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667n + n2 = 116.6666667 + 1.777777780 Combine like terms: 116.6666667 + 1.777777780 = 118.44444448 1.777777780 + 2.666666667n + n2 = 118.44444448 Factor a perfect square on the left side: (n + 1.333333334)(n + 1.333333334) = 118.44444448 Calculate the square root of the right side: 10.88321848 Break this problem into two subproblems by setting (n + 1.333333334) equal to 10.88321848 and -10.88321848.Subproblem 1
n + 1.333333334 = 10.88321848 Simplifying n + 1.333333334 = 10.88321848 Reorder the terms: 1.333333334 + n = 10.88321848 Solving 1.333333334 + n = 10.88321848 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + n = 10.88321848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + n = 10.88321848 + -1.333333334 n = 10.88321848 + -1.333333334 Combine like terms: 10.88321848 + -1.333333334 = 9.549885146 n = 9.549885146 Simplifying n = 9.549885146Subproblem 2
n + 1.333333334 = -10.88321848 Simplifying n + 1.333333334 = -10.88321848 Reorder the terms: 1.333333334 + n = -10.88321848 Solving 1.333333334 + n = -10.88321848 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + n = -10.88321848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + n = -10.88321848 + -1.333333334 n = -10.88321848 + -1.333333334 Combine like terms: -10.88321848 + -1.333333334 = -12.216551814 n = -12.216551814 Simplifying n = -12.216551814Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.549885146, -12.216551814}Solution
n = {9.549885146, -12.216551814}
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