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Simplifying 15n2 + -1n = 72 Reorder the terms: -1n + 15n2 = 72 Solving -1n + 15n2 = 72 Solving for variable 'n'. Reorder the terms: -72 + -1n + 15n2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -1n + 15n2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.8 + -0.06666666667n + n2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -0.06666666667n + 4.8 + n2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -0.06666666667n + n2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -0.06666666667n + n2 = 0 + 4.8 -0.06666666667n + n2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -0.06666666667n + n2 = 4.8 The n term is -0.06666666667n. Take half its coefficient (-0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. -0.06666666667n + 0.001111111112 + n2 = 4.8 + 0.001111111112 Reorder the terms: 0.001111111112 + -0.06666666667n + n2 = 4.8 + 0.001111111112 Combine like terms: 4.8 + 0.001111111112 = 4.801111111112 0.001111111112 + -0.06666666667n + n2 = 4.801111111112 Factor a perfect square on the left side: (n + -0.03333333334)(n + -0.03333333334) = 4.801111111112 Calculate the square root of the right side: 2.191143791 Break this problem into two subproblems by setting (n + -0.03333333334) equal to 2.191143791 and -2.191143791.Subproblem 1
n + -0.03333333334 = 2.191143791 Simplifying n + -0.03333333334 = 2.191143791 Reorder the terms: -0.03333333334 + n = 2.191143791 Solving -0.03333333334 + n = 2.191143791 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + n = 2.191143791 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + n = 2.191143791 + 0.03333333334 n = 2.191143791 + 0.03333333334 Combine like terms: 2.191143791 + 0.03333333334 = 2.22447712434 n = 2.22447712434 Simplifying n = 2.22447712434Subproblem 2
n + -0.03333333334 = -2.191143791 Simplifying n + -0.03333333334 = -2.191143791 Reorder the terms: -0.03333333334 + n = -2.191143791 Solving -0.03333333334 + n = -2.191143791 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + n = -2.191143791 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + n = -2.191143791 + 0.03333333334 n = -2.191143791 + 0.03333333334 Combine like terms: -2.191143791 + 0.03333333334 = -2.15781045766 n = -2.15781045766 Simplifying n = -2.15781045766Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.22447712434, -2.15781045766}
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