Solve 238-1000102 r^2

Question

Factor the expression

2 (119 - 500051 r^{2})

Evaluate

238 - 1000102 r^{2}

Solution

2 (119 - 500051 r^{2})

Show Solution

r_{1} = - \frac{59506069}{500051}, r_{2} = \frac{59506069}{500051}

Alternative Form

r_{1} \approx - 0.015426, r_{2} \approx 0.015426

Evaluate

238 - 1000102 r^{2}

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

238 - 1000102 r^{2} = 0

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

- 1000102 r^{2} = 0 - 238

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

- 1000102 r^{2} = - 238

Change the signs on both sides of the equation

1000102 r^{2} = 238

Divide both sides

\frac{1000102 r ^{2}}{1000102} = \frac{238}{1000102}

Divide the numbers

r^{2} = \frac{238}{1000102}

Cancel out the common factor 2

r^{2} = \frac{119}{500051}

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

r = \pm \frac{119}{500051}

Simplify the expression

More Steps

Evaluate

\frac{119}{500051}

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

\frac{119}{500051}

Multiply by the Conjugate

\frac{119 \times 500051}{500051 \times 500051}

Multiply the numbers

More Steps

Evaluate

119 \times 500051

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

119 \times 500051

Calculate the product

59506069

\frac{59506069}{500051 \times 500051}

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

\frac{59506069}{500051}

r = \pm \frac{59506069}{500051}

Separate the equation into 2 possible cases

r = \frac{59506069}{500051} r = - \frac{59506069}{500051}

Solution

r_{1} = - \frac{59506069}{500051}, r_{2} = \frac{59506069}{500051}

Alternative Form

r_{1} \approx - 0.015426, r_{2} \approx 0.015426

Show Solution