Solve k1712k-13 - ScanMath

Question

Simplify the expression

1712 k^{2} - 13

Evaluate

k \times 1712 k - 13

Solution

More Steps

Evaluate

k \times 1712 k

Multiply the terms

k^{2} \times 1712

Use the commutative property to reorder the terms

1712 k^{2}

1712 k^{2} - 13

Show Solution

k_{1} = - \frac{1391}{428}, k_{2} = \frac{1391}{428}

Alternative Form

k_{1} \approx - 0.08714, k_{2} \approx 0.08714

Evaluate

k \times 1712 k - 13

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

k \times 1712 k - 13 = 0

Multiply

More Steps

Multiply the terms

k \times 1712 k

Multiply the terms

k^{2} \times 1712

Use the commutative property to reorder the terms

1712 k^{2}

1712 k^{2} - 13 = 0

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

1712 k^{2} = 0 + 13

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

1712 k^{2} = 13

Divide both sides

\frac{1712 k ^{2}}{1712} = \frac{13}{1712}

Divide the numbers

k^{2} = \frac{13}{1712}

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

k = \pm \frac{13}{1712}

Simplify the expression

More Steps

Evaluate

\frac{13}{1712}

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

\frac{13}{1712}

Simplify the radical expression

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Evaluate

1712

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

16 \times 107

Write the number in exponential form with the base of 4

4^{2} \times 107

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

4^{2} \times 107

Reduce the index of the radical and exponent with 2

4107

\frac{13}{4 107}

Multiply by the Conjugate

\frac{13 \times 107}{4 107 \times 107}

Multiply the numbers

More Steps

Evaluate

13 \times 107

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

13 \times 107

Calculate the product

1391

\frac{1391}{4 107 \times 107}

Multiply the numbers

More Steps

Evaluate

4107 \times 107

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

4 \times 107

Multiply the terms

428

\frac{1391}{428}

k = \pm \frac{1391}{428}

Separate the equation into 2 possible cases

k = \frac{1391}{428} k = - \frac{1391}{428}

Solution

k_{1} = - \frac{1391}{428}, k_{2} = \frac{1391}{428}

Alternative Form

k_{1} \approx - 0.08714, k_{2} \approx 0.08714

Show Solution