Solve 1a^23-70-100

Question

Simplify the expression

3 a^{2} - 170

Evaluate

1 \times a^{2} \times 3 - 70 - 100

Multiply the terms

More Steps

Multiply the terms

1 \times a^{2} \times 3

Rewrite the expression

a^{2} \times 3

Use the commutative property to reorder the terms

3 a^{2}

3 a^{2} - 70 - 100

Solution

3 a^{2} - 170

Show Solution

a_{1} = - \frac{510}{3}, a_{2} = \frac{510}{3}

Alternative Form

a_{1} \approx - 7.527727, a_{2} \approx 7.527727

Evaluate

1 \times a^{2} \times 3 - 70 - 100

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

1 \times a^{2} \times 3 - 70 - 100 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times a^{2} \times 3

Rewrite the expression

a^{2} \times 3

Use the commutative property to reorder the terms

3 a^{2}

3 a^{2} - 70 - 100 = 0

Subtract the numbers

3 a^{2} - 170 = 0

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

3 a^{2} = 0 + 170

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

3 a^{2} = 170

Divide both sides

\frac{3 a ^{2}}{3} = \frac{170}{3}

Divide the numbers

a^{2} = \frac{170}{3}

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

a = \pm \frac{170}{3}

Simplify the expression

More Steps

Evaluate

\frac{170}{3}

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

\frac{170}{3}

Multiply by the Conjugate

\frac{170 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

170 \times 3

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

170 \times 3

Calculate the product

510

\frac{510}{3 \times 3}

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

\frac{510}{3}

a = \pm \frac{510}{3}

Separate the equation into 2 possible cases

a = \frac{510}{3} a = - \frac{510}{3}

Solution

a_{1} = - \frac{510}{3}, a_{2} = \frac{510}{3}

Alternative Form

a_{1} \approx - 7.527727, a_{2} \approx 7.527727

Show Solution