Solve v^24-50018 - ScanMath

Question

Simplify the expression

4 v^{2} - 50018

Evaluate

v^{2} \times 4 - 50018

Solution

4 v^{2} - 50018

Show Solution

2 (2 v^{2} - 25009)

Evaluate

v^{2} \times 4 - 50018

Use the commutative property to reorder the terms

4 v^{2} - 50018

Solution

2 (2 v^{2} - 25009)

Show Solution

v_{1} = - \frac{50018}{2}, v_{2} = \frac{50018}{2}

Alternative Form

v_{1} \approx - 111.823522, v_{2} \approx 111.823522

Evaluate

v^{2} \times 4 - 50018

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

v^{2} \times 4 - 50018 = 0

Use the commutative property to reorder the terms

4 v^{2} - 50018 = 0

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

4 v^{2} = 0 + 50018

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

4 v^{2} = 50018

Divide both sides

\frac{4 v ^{2}}{4} = \frac{50018}{4}

Divide the numbers

v^{2} = \frac{50018}{4}

Cancel out the common factor 2

v^{2} = \frac{25009}{2}

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

v = \pm \frac{25009}{2}

Simplify the expression

More Steps

Evaluate

\frac{25009}{2}

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

\frac{25009}{2}

Multiply by the Conjugate

\frac{25009 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

25009 \times 2

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

25009 \times 2

Calculate the product

50018

\frac{50018}{2 \times 2}

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

\frac{50018}{2}

v = \pm \frac{50018}{2}

Separate the equation into 2 possible cases

v = \frac{50018}{2} v = - \frac{50018}{2}

Solution

v_{1} = - \frac{50018}{2}, v_{2} = \frac{50018}{2}

Alternative Form

v_{1} \approx - 111.823522, v_{2} \approx 111.823522

Show Solution