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Simplifying n2 + -4n + 5n + -20 = 5 Reorder the terms: -20 + -4n + 5n + n2 = 5 Combine like terms: -4n + 5n = 1n -20 + 1n + n2 = 5 Solving -20 + 1n + n2 = 5 Solving for variable 'n'. Reorder the terms: -20 + -5 + 1n + n2 = 5 + -5 Combine like terms: -20 + -5 = -25 -25 + 1n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -25 + 1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 1n + 25 + n2 = 0 + 25 Reorder the terms: -25 + 25 + 1n + n2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1n + n2 = 0 + 25 1n + n2 = 0 + 25 Combine like terms: 0 + 25 = 25 1n + n2 = 25 The n term is 1n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 25 + 0.25 Reorder the terms: 0.25 + n + n2 = 25 + 0.25 Combine like terms: 25 + 0.25 = 25.25 0.25 + n + n2 = 25.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (n + 0.5) equal to 5.024937811 and -5.024937811.Subproblem 1
n + 0.5 = 5.024937811 Simplifying n + 0.5 = 5.024937811 Reorder the terms: 0.5 + n = 5.024937811 Solving 0.5 + n = 5.024937811 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 5.024937811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 5.024937811 + -0.5 n = 5.024937811 + -0.5 Combine like terms: 5.024937811 + -0.5 = 4.524937811 n = 4.524937811 Simplifying n = 4.524937811Subproblem 2
n + 0.5 = -5.024937811 Simplifying n + 0.5 = -5.024937811 Reorder the terms: 0.5 + n = -5.024937811 Solving 0.5 + n = -5.024937811 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -5.024937811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -5.024937811 + -0.5 n = -5.024937811 + -0.5 Combine like terms: -5.024937811 + -0.5 = -5.524937811 n = -5.524937811 Simplifying n = -5.524937811Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.524937811, -5.524937811}
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