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Simplifying 10n2 + 12n + -21 = 0 Reorder the terms: -21 + 12n + 10n2 = 0 Solving -21 + 12n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + 1.2n + n2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 1.2n + 2.1 + n2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + 1.2n + n2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 1.2n + n2 = 0 + 2.1 1.2n + n2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 1.2n + n2 = 2.1 The n term is 1.2n. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2n + 0.36 + n2 = 2.1 + 0.36 Reorder the terms: 0.36 + 1.2n + n2 = 2.1 + 0.36 Combine like terms: 2.1 + 0.36 = 2.46 0.36 + 1.2n + n2 = 2.46 Factor a perfect square on the left side: (n + 0.6)(n + 0.6) = 2.46 Calculate the square root of the right side: 1.568438714 Break this problem into two subproblems by setting (n + 0.6) equal to 1.568438714 and -1.568438714.Subproblem 1
n + 0.6 = 1.568438714 Simplifying n + 0.6 = 1.568438714 Reorder the terms: 0.6 + n = 1.568438714 Solving 0.6 + n = 1.568438714 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = 1.568438714 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = 1.568438714 + -0.6 n = 1.568438714 + -0.6 Combine like terms: 1.568438714 + -0.6 = 0.968438714 n = 0.968438714 Simplifying n = 0.968438714Subproblem 2
n + 0.6 = -1.568438714 Simplifying n + 0.6 = -1.568438714 Reorder the terms: 0.6 + n = -1.568438714 Solving 0.6 + n = -1.568438714 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = -1.568438714 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = -1.568438714 + -0.6 n = -1.568438714 + -0.6 Combine like terms: -1.568438714 + -0.6 = -2.168438714 n = -2.168438714 Simplifying n = -2.168438714Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.968438714, -2.168438714}
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