Solve d^2122-15010

Question

Simplify the expression

122 d^{2} - 15010

Evaluate

d^{2} \times 122 - 15010

Solution

122 d^{2} - 15010

Show Solution

2 (61 d^{2} - 7505)

Evaluate

d^{2} \times 122 - 15010

Use the commutative property to reorder the terms

122 d^{2} - 15010

Solution

2 (61 d^{2} - 7505)

Show Solution

d_{1} = - \frac{457805}{61}, d_{2} = \frac{457805}{61}

Alternative Form

d_{1} \approx - 11.092015, d_{2} \approx 11.092015

Evaluate

d^{2} \times 122 - 15010

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

d^{2} \times 122 - 15010 = 0

Use the commutative property to reorder the terms

122 d^{2} - 15010 = 0

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

122 d^{2} = 0 + 15010

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

122 d^{2} = 15010

Divide both sides

\frac{122 d ^{2}}{122} = \frac{15010}{122}

Divide the numbers

d^{2} = \frac{15010}{122}

Cancel out the common factor 2

d^{2} = \frac{7505}{61}

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

d = \pm \frac{7505}{61}

Simplify the expression

More Steps

Evaluate

\frac{7505}{61}

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

\frac{7505}{61}

Multiply by the Conjugate

\frac{7505 \times 61}{61 \times 61}

Multiply the numbers

More Steps

Evaluate

7505 \times 61

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

7505 \times 61

Calculate the product

457805

\frac{457805}{61 \times 61}

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

\frac{457805}{61}

d = \pm \frac{457805}{61}

Separate the equation into 2 possible cases

d = \frac{457805}{61} d = - \frac{457805}{61}

Solution

d_{1} = - \frac{457805}{61}, d_{2} = \frac{457805}{61}

Alternative Form

d_{1} \approx - 11.092015, d_{2} \approx 11.092015

Show Solution