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Simplifying 4n2 + -6n + -7 = 0 Reorder the terms: -7 + -6n + 4n2 = 0 Solving -7 + -6n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -1.5n + n2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.5n + 1.75 + n2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.5n + n2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.5n + n2 = 0 + 1.75 -1.5n + n2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.5n + n2 = 1.75 The n term is -1.5n. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5n + 0.5625 + n2 = 1.75 + 0.5625 Reorder the terms: 0.5625 + -1.5n + n2 = 1.75 + 0.5625 Combine like terms: 1.75 + 0.5625 = 2.3125 0.5625 + -1.5n + n2 = 2.3125 Factor a perfect square on the left side: (n + -0.75)(n + -0.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (n + -0.75) equal to 1.520690633 and -1.520690633.Subproblem 1
n + -0.75 = 1.520690633 Simplifying n + -0.75 = 1.520690633 Reorder the terms: -0.75 + n = 1.520690633 Solving -0.75 + n = 1.520690633 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = 1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = 1.520690633 + 0.75 n = 1.520690633 + 0.75 Combine like terms: 1.520690633 + 0.75 = 2.270690633 n = 2.270690633 Simplifying n = 2.270690633Subproblem 2
n + -0.75 = -1.520690633 Simplifying n + -0.75 = -1.520690633 Reorder the terms: -0.75 + n = -1.520690633 Solving -0.75 + n = -1.520690633 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = -1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = -1.520690633 + 0.75 n = -1.520690633 + 0.75 Combine like terms: -1.520690633 + 0.75 = -0.770690633 n = -0.770690633 Simplifying n = -0.770690633Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.270690633, -0.770690633}
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