What is the answer to (5k-1)^{-2}=k+5 ?

The answer to (5k-1)^{-2}=k+5 is k\approx 0.11153…,k\approx 0.28698…,k\approx-4.99851…

Solve for k: (5k-1)^{-2}=k+5

The solution is k\approx 0.11153…,k\approx 0.28698…,k\approx-4.99851…

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(5 k - 1)^{- 2} = k + 5

k \approx 0.11153 \dots, k \approx 0.28698 \dots, k \approx - 4.99851 \dots

Solution steps

(5 k - 1)^{- 2} = k + 5

Refine

\frac{1}{( 5 k - 1 ) ^{2}} = k + 5

Multiply both sides by

(5 k - 1)^{2}

1 = k (5 k - 1)^{2} + 5 (5 k - 1)^{2}

Solve

1 = k (5 k - 1)^{2} + 5 (5 k - 1)^{2} : k \approx 0.11153 \dots, k \approx 0.28698 \dots, k \approx - 4.99851 \dots

k \approx 0.11153 \dots, k \approx 0.28698 \dots, k \approx - 4.99851 \dots

Verify Solutions

Find undefined (singularity) points:

k = \frac{1}{5}

Combine undefined points with solutions:

k \approx 0.11153 \dots, k \approx 0.28698 \dots, k \approx - 4.99851 \dots

1 = \frac{10 x ^{2}}{x ^{4} + 25}

\frac{x + 1}{x ^{2} - 3} = 3

y, x = \frac{3}{2 y - 4}

\frac{3}{z} = \frac{9}{12}

7 - \frac{1}{t} = \frac{6}{t ^{2}}

What is the answer to (5k-1)^{-2}=k+5 ?
The answer to (5k-1)^{-2}=k+5 is k\approx 0.11153…,k\approx 0.28698…,k\approx-4.99851…
Solve for k: (5k-1)^{-2}=k+5
The solution is k\approx 0.11153…,k\approx 0.28698…,k\approx-4.99851…