Solve k^22-100 - ScanMath

Question

Simplify the expression

2 k^{2} - 100

Evaluate

k^{2} \times 2 - 100

Solution

2 k^{2} - 100

Show Solution

2 (k^{2} - 50)

Evaluate

k^{2} \times 2 - 100

Use the commutative property to reorder the terms

2 k^{2} - 100

Solution

2 (k^{2} - 50)

Show Solution

k_{1} = - 52, k_{2} = 52

Alternative Form

k_{1} \approx - 7.071068, k_{2} \approx 7.071068

Evaluate

k^{2} \times 2 - 100

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

k^{2} \times 2 - 100 = 0

Use the commutative property to reorder the terms

2 k^{2} - 100 = 0

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

2 k^{2} = 0 + 100

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

2 k^{2} = 100

Divide both sides

\frac{2 k ^{2}}{2} = \frac{100}{2}

Divide the numbers

k^{2} = \frac{100}{2}

Divide the numbers

More Steps

Evaluate

\frac{100}{2}

Reduce the numbers

\frac{50}{1}

Calculate

50

k^{2} = 50

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

k = \pm 50

Simplify the expression

More Steps

Evaluate

50

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

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

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

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

k = \pm 52

Separate the equation into 2 possible cases

k = 52 k = - 52

Solution

k_{1} = - 52, k_{2} = 52

Alternative Form

k_{1} \approx - 7.071068, k_{2} \approx 7.071068

Show Solution