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Simplifying 10n2 + -7n + -4 = 0 Reorder the terms: -4 + -7n + 10n2 = 0 Solving -4 + -7n + 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'. -0.4 + -0.7n + n2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.7n + 0.4 + n2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.7n + n2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.7n + n2 = 0 + 0.4 -0.7n + n2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.7n + n2 = 0.4 The n term is -0.7n. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7n + 0.1225 + n2 = 0.4 + 0.1225 Reorder the terms: 0.1225 + -0.7n + n2 = 0.4 + 0.1225 Combine like terms: 0.4 + 0.1225 = 0.5225 0.1225 + -0.7n + n2 = 0.5225 Factor a perfect square on the left side: (n + -0.35)(n + -0.35) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (n + -0.35) equal to 0.722841615 and -0.722841615.Subproblem 1
n + -0.35 = 0.722841615 Simplifying n + -0.35 = 0.722841615 Reorder the terms: -0.35 + n = 0.722841615 Solving -0.35 + n = 0.722841615 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + n = 0.722841615 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + n = 0.722841615 + 0.35 n = 0.722841615 + 0.35 Combine like terms: 0.722841615 + 0.35 = 1.072841615 n = 1.072841615 Simplifying n = 1.072841615Subproblem 2
n + -0.35 = -0.722841615 Simplifying n + -0.35 = -0.722841615 Reorder the terms: -0.35 + n = -0.722841615 Solving -0.35 + n = -0.722841615 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + n = -0.722841615 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + n = -0.722841615 + 0.35 n = -0.722841615 + 0.35 Combine like terms: -0.722841615 + 0.35 = -0.372841615 n = -0.372841615 Simplifying n = -0.372841615Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.072841615, -0.372841615}
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