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Simplifying 10n2 + 12n + -3 = 0 Reorder the terms: -3 + 12n + 10n2 = 0 Solving -3 + 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'. -0.3 + 1.2n + n2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.2n + 0.3 + n2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.2n + n2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.2n + n2 = 0 + 0.3 1.2n + n2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 1.2n + n2 = 0.3 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 = 0.3 + 0.36 Reorder the terms: 0.36 + 1.2n + n2 = 0.3 + 0.36 Combine like terms: 0.3 + 0.36 = 0.66 0.36 + 1.2n + n2 = 0.66 Factor a perfect square on the left side: (n + 0.6)(n + 0.6) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (n + 0.6) equal to 0.81240384 and -0.81240384.Subproblem 1
n + 0.6 = 0.81240384 Simplifying n + 0.6 = 0.81240384 Reorder the terms: 0.6 + n = 0.81240384 Solving 0.6 + n = 0.81240384 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 = 0.81240384 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = 0.81240384 + -0.6 n = 0.81240384 + -0.6 Combine like terms: 0.81240384 + -0.6 = 0.21240384 n = 0.21240384 Simplifying n = 0.21240384Subproblem 2
n + 0.6 = -0.81240384 Simplifying n + 0.6 = -0.81240384 Reorder the terms: 0.6 + n = -0.81240384 Solving 0.6 + n = -0.81240384 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 = -0.81240384 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = -0.81240384 + -0.6 n = -0.81240384 + -0.6 Combine like terms: -0.81240384 + -0.6 = -1.41240384 n = -1.41240384 Simplifying n = -1.41240384Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.21240384, -1.41240384}
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