Solve k^2393-26/14

Question

Simplify the expression

393 k^{2} - \frac{13}{7}

Evaluate

k^{2} \times 393 - \frac{26}{14}

Cancel out the common factor 2

k^{2} \times 393 - \frac{13}{7}

Solution

393 k^{2} - \frac{13}{7}

Show Solution

\frac{1}{7} (2751 k^{2} - 13)

Evaluate

k^{2} \times 393 - \frac{26}{14}

Cancel out the common factor 2

k^{2} \times 393 - \frac{13}{7}

Use the commutative property to reorder the terms

393 k^{2} - \frac{13}{7}

Solution

\frac{1}{7} (2751 k^{2} - 13)

Show Solution

k_{1} = - \frac{35763}{2751}, k_{2} = \frac{35763}{2751}

Alternative Form

k_{1} \approx - 0.068743, k_{2} \approx 0.068743

Evaluate

k^{2} \times 393 - \frac{26}{14}

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

k^{2} \times 393 - \frac{26}{14} = 0

Cancel out the common factor 2

k^{2} \times 393 - \frac{13}{7} = 0

Use the commutative property to reorder the terms

393 k^{2} - \frac{13}{7} = 0

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

393 k^{2} = 0 + \frac{13}{7}

Add the terms

393 k^{2} = \frac{13}{7}

Multiply by the reciprocal

393 k^{2} \times \frac{1}{393} = \frac{13}{7} \times \frac{1}{393}

Multiply

k^{2} = \frac{13}{7} \times \frac{1}{393}

Multiply

More Steps

Evaluate

\frac{13}{7} \times \frac{1}{393}

To multiply the fractions,multiply the numerators and denominators separately

\frac{13}{7 \times 393}

Multiply the numbers

\frac{13}{2751}

k^{2} = \frac{13}{2751}

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

k = \pm \frac{13}{2751}

Simplify the expression

More Steps

Evaluate

\frac{13}{2751}

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

\frac{13}{2751}

Multiply by the Conjugate

\frac{13 \times 2751}{2751 \times 2751}

Multiply the numbers

More Steps

Evaluate

13 \times 2751

The product of roots with the same index is equal to the root of the product

13 \times 2751

Calculate the product

35763

\frac{35763}{2751 \times 2751}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{35763}{2751}

k = \pm \frac{35763}{2751}

Separate the equation into 2 possible cases

k = \frac{35763}{2751} k = - \frac{35763}{2751}

Solution

k_{1} = - \frac{35763}{2751}, k_{2} = \frac{35763}{2751}

Alternative Form

k_{1} \approx - 0.068743, k_{2} \approx 0.068743

Show Solution