Solve 69725-4k^24

Question

Simplify the expression

69725 - 16 k^{2}

Evaluate

69725 - 4 k^{2} \times 4

Solution

69725 - 16 k^{2}

Show Solution

k_{1} = - \frac{5 2789}{4}, k_{2} = \frac{5 2789}{4}

Alternative Form

k_{1} \approx - 66.01373, k_{2} \approx 66.01373

Evaluate

69725 - 4 k^{2} \times 4

To find the roots of the expression,set the expression equal to 0

69725 - 4 k^{2} \times 4 = 0

Multiply the terms

69725 - 16 k^{2} = 0

Move the constant to the right-hand side and change its sign

- 16 k^{2} = 0 - 69725

Removing 0 doesn't change the value,so remove it from the expression

- 16 k^{2} = - 69725

Change the signs on both sides of the equation

16 k^{2} = 69725

Divide both sides

\frac{16 k ^{2}}{16} = \frac{69725}{16}

Divide the numbers

k^{2} = \frac{69725}{16}

Take the root of both sides of the equation and remember to use both positive and negative roots

k = \pm \frac{69725}{16}

Simplify the expression

More Steps

Evaluate

\frac{69725}{16}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{69725}{16}

Simplify the radical expression

More Steps

Evaluate

69725

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2789

Write the number in exponential form with the base of 5

5^{2} \times 2789

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2789

Reduce the index of the radical and exponent with 2

52789

\frac{5 2789}{16}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{5 2789}{4}

k = \pm \frac{5 2789}{4}

Separate the equation into 2 possible cases

k = \frac{5 2789}{4} k = - \frac{5 2789}{4}

Solution

k_{1} = - \frac{5 2789}{4}, k_{2} = \frac{5 2789}{4}

Alternative Form

k_{1} \approx - 66.01373, k_{2} \approx 66.01373

Show Solution