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Simplifying 21n2 + -38n = 38 Reorder the terms: -38n + 21n2 = 38 Solving -38n + 21n2 = 38 Solving for variable 'n'. Reorder the terms: -38 + -38n + 21n2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -38n + 21n2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.80952381 + -1.80952381n + n2 = 0 Move the constant term to the right: Add '1.80952381' to each side of the equation. -1.80952381 + -1.80952381n + 1.80952381 + n2 = 0 + 1.80952381 Reorder the terms: -1.80952381 + 1.80952381 + -1.80952381n + n2 = 0 + 1.80952381 Combine like terms: -1.80952381 + 1.80952381 = 0.00000000 0.00000000 + -1.80952381n + n2 = 0 + 1.80952381 -1.80952381n + n2 = 0 + 1.80952381 Combine like terms: 0 + 1.80952381 = 1.80952381 -1.80952381n + n2 = 1.80952381 The n term is -1.80952381n. Take half its coefficient (-0.904761905). Square it (0.8185941047) and add it to both sides. Add '0.8185941047' to each side of the equation. -1.80952381n + 0.8185941047 + n2 = 1.80952381 + 0.8185941047 Reorder the terms: 0.8185941047 + -1.80952381n + n2 = 1.80952381 + 0.8185941047 Combine like terms: 1.80952381 + 0.8185941047 = 2.6281179147 0.8185941047 + -1.80952381n + n2 = 2.6281179147 Factor a perfect square on the left side: (n + -0.904761905)(n + -0.904761905) = 2.6281179147 Calculate the square root of the right side: 1.621147098 Break this problem into two subproblems by setting (n + -0.904761905) equal to 1.621147098 and -1.621147098.Subproblem 1
n + -0.904761905 = 1.621147098 Simplifying n + -0.904761905 = 1.621147098 Reorder the terms: -0.904761905 + n = 1.621147098 Solving -0.904761905 + n = 1.621147098 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.904761905' to each side of the equation. -0.904761905 + 0.904761905 + n = 1.621147098 + 0.904761905 Combine like terms: -0.904761905 + 0.904761905 = 0.000000000 0.000000000 + n = 1.621147098 + 0.904761905 n = 1.621147098 + 0.904761905 Combine like terms: 1.621147098 + 0.904761905 = 2.525909003 n = 2.525909003 Simplifying n = 2.525909003Subproblem 2
n + -0.904761905 = -1.621147098 Simplifying n + -0.904761905 = -1.621147098 Reorder the terms: -0.904761905 + n = -1.621147098 Solving -0.904761905 + n = -1.621147098 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.904761905' to each side of the equation. -0.904761905 + 0.904761905 + n = -1.621147098 + 0.904761905 Combine like terms: -0.904761905 + 0.904761905 = 0.000000000 0.000000000 + n = -1.621147098 + 0.904761905 n = -1.621147098 + 0.904761905 Combine like terms: -1.621147098 + 0.904761905 = -0.716385193 n = -0.716385193 Simplifying n = -0.716385193Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.525909003, -0.716385193}
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