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Simplifying 4n2 + -7n + -9 = 0 Reorder the terms: -9 + -7n + 4n2 = 0 Solving -9 + -7n + 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'. -2.25 + -1.75n + n2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.75n + 2.25 + n2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.75n + n2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.75n + n2 = 0 + 2.25 -1.75n + n2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.75n + n2 = 2.25 The n term is -1.75n. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75n + 0.765625 + n2 = 2.25 + 0.765625 Reorder the terms: 0.765625 + -1.75n + n2 = 2.25 + 0.765625 Combine like terms: 2.25 + 0.765625 = 3.015625 0.765625 + -1.75n + n2 = 3.015625 Factor a perfect square on the left side: (n + -0.875)(n + -0.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (n + -0.875) equal to 1.736555499 and -1.736555499.Subproblem 1
n + -0.875 = 1.736555499 Simplifying n + -0.875 = 1.736555499 Reorder the terms: -0.875 + n = 1.736555499 Solving -0.875 + n = 1.736555499 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + n = 1.736555499 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = 1.736555499 + 0.875 n = 1.736555499 + 0.875 Combine like terms: 1.736555499 + 0.875 = 2.611555499 n = 2.611555499 Simplifying n = 2.611555499Subproblem 2
n + -0.875 = -1.736555499 Simplifying n + -0.875 = -1.736555499 Reorder the terms: -0.875 + n = -1.736555499 Solving -0.875 + n = -1.736555499 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + n = -1.736555499 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = -1.736555499 + 0.875 n = -1.736555499 + 0.875 Combine like terms: -1.736555499 + 0.875 = -0.861555499 n = -0.861555499 Simplifying n = -0.861555499Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.611555499, -0.861555499}
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