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Simplifying n2 + n + -4n + -4 = 70 Reorder the terms: -4 + n + -4n + n2 = 70 Combine like terms: n + -4n = -3n -4 + -3n + n2 = 70 Solving -4 + -3n + n2 = 70 Solving for variable 'n'. Reorder the terms: -4 + -70 + -3n + n2 = 70 + -70 Combine like terms: -4 + -70 = -74 -74 + -3n + n2 = 70 + -70 Combine like terms: 70 + -70 = 0 -74 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -3n + 74 + n2 = 0 + 74 Reorder the terms: -74 + 74 + -3n + n2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -3n + n2 = 0 + 74 -3n + n2 = 0 + 74 Combine like terms: 0 + 74 = 74 -3n + n2 = 74 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 74 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 74 + 2.25 Combine like terms: 74 + 2.25 = 76.25 2.25 + -3n + n2 = 76.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (n + -1.5) equal to 8.732124598 and -8.732124598.Subproblem 1
n + -1.5 = 8.732124598 Simplifying n + -1.5 = 8.732124598 Reorder the terms: -1.5 + n = 8.732124598 Solving -1.5 + n = 8.732124598 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 8.732124598 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 8.732124598 + 1.5 n = 8.732124598 + 1.5 Combine like terms: 8.732124598 + 1.5 = 10.232124598 n = 10.232124598 Simplifying n = 10.232124598Subproblem 2
n + -1.5 = -8.732124598 Simplifying n + -1.5 = -8.732124598 Reorder the terms: -1.5 + n = -8.732124598 Solving -1.5 + n = -8.732124598 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -8.732124598 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -8.732124598 + 1.5 n = -8.732124598 + 1.5 Combine like terms: -8.732124598 + 1.5 = -7.232124598 n = -7.232124598 Simplifying n = -7.232124598Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.232124598, -7.232124598}
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