Solve a 154a-3 - ScanMath

Question

Simplify the expression

154 a^{2} - 3

Evaluate

a \times 154 a - 3

Solution

More Steps

Evaluate

a \times 154 a

Multiply the terms

a^{2} \times 154

Use the commutative property to reorder the terms

154 a^{2}

154 a^{2} - 3

Show Solution

a_{1} = - \frac{462}{154}, a_{2} = \frac{462}{154}

Alternative Form

a_{1} \approx - 0.139573, a_{2} \approx 0.139573

Evaluate

a \times 154 a - 3

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

a \times 154 a - 3 = 0

Multiply

More Steps

Multiply the terms

a \times 154 a

Multiply the terms

a^{2} \times 154

Use the commutative property to reorder the terms

154 a^{2}

154 a^{2} - 3 = 0

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

154 a^{2} = 0 + 3

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

154 a^{2} = 3

Divide both sides

\frac{154 a ^{2}}{154} = \frac{3}{154}

Divide the numbers

a^{2} = \frac{3}{154}

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

a = \pm \frac{3}{154}

Simplify the expression

More Steps

Evaluate

\frac{3}{154}

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

\frac{3}{154}

Multiply by the Conjugate

\frac{3 \times 154}{154 \times 154}

Multiply the numbers

More Steps

Evaluate

3 \times 154

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

3 \times 154

Calculate the product

462

\frac{462}{154 \times 154}

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

\frac{462}{154}

a = \pm \frac{462}{154}

Separate the equation into 2 possible cases

a = \frac{462}{154} a = - \frac{462}{154}

Solution

a_{1} = - \frac{462}{154}, a_{2} = \frac{462}{154}

Alternative Form

a_{1} \approx - 0.139573, a_{2} \approx 0.139573

Show Solution