175n^2-430n-240=0

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Solution for 175n^2-430n-240=0 equation:


Simplifying
175n2 + -430n + -240 = 0

Reorder the terms:
-240 + -430n + 175n2 = 0

Solving
-240 + -430n + 175n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-48 + -86n + 35n2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-48 + -86n + 35n2)' equal to zero and attempt to solve: Simplifying -48 + -86n + 35n2 = 0 Solving -48 + -86n + 35n2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.371428571 + -2.457142857n + n2 = 0 Move the constant term to the right: Add '1.371428571' to each side of the equation. -1.371428571 + -2.457142857n + 1.371428571 + n2 = 0 + 1.371428571 Reorder the terms: -1.371428571 + 1.371428571 + -2.457142857n + n2 = 0 + 1.371428571 Combine like terms: -1.371428571 + 1.371428571 = 0.000000000 0.000000000 + -2.457142857n + n2 = 0 + 1.371428571 -2.457142857n + n2 = 0 + 1.371428571 Combine like terms: 0 + 1.371428571 = 1.371428571 -2.457142857n + n2 = 1.371428571 The n term is -2.457142857n. Take half its coefficient (-1.228571429). Square it (1.509387756) and add it to both sides. Add '1.509387756' to each side of the equation. -2.457142857n + 1.509387756 + n2 = 1.371428571 + 1.509387756 Reorder the terms: 1.509387756 + -2.457142857n + n2 = 1.371428571 + 1.509387756 Combine like terms: 1.371428571 + 1.509387756 = 2.880816327 1.509387756 + -2.457142857n + n2 = 2.880816327 Factor a perfect square on the left side: (n + -1.228571429)(n + -1.228571429) = 2.880816327 Calculate the square root of the right side: 1.69729677 Break this problem into two subproblems by setting (n + -1.228571429) equal to 1.69729677 and -1.69729677.

Subproblem 1

n + -1.228571429 = 1.69729677 Simplifying n + -1.228571429 = 1.69729677 Reorder the terms: -1.228571429 + n = 1.69729677 Solving -1.228571429 + n = 1.69729677 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.228571429' to each side of the equation. -1.228571429 + 1.228571429 + n = 1.69729677 + 1.228571429 Combine like terms: -1.228571429 + 1.228571429 = 0.000000000 0.000000000 + n = 1.69729677 + 1.228571429 n = 1.69729677 + 1.228571429 Combine like terms: 1.69729677 + 1.228571429 = 2.925868199 n = 2.925868199 Simplifying n = 2.925868199

Subproblem 2

n + -1.228571429 = -1.69729677 Simplifying n + -1.228571429 = -1.69729677 Reorder the terms: -1.228571429 + n = -1.69729677 Solving -1.228571429 + n = -1.69729677 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.228571429' to each side of the equation. -1.228571429 + 1.228571429 + n = -1.69729677 + 1.228571429 Combine like terms: -1.228571429 + 1.228571429 = 0.000000000 0.000000000 + n = -1.69729677 + 1.228571429 n = -1.69729677 + 1.228571429 Combine like terms: -1.69729677 + 1.228571429 = -0.468725341 n = -0.468725341 Simplifying n = -0.468725341

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.925868199, -0.468725341}

Solution

n = {2.925868199, -0.468725341}

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