Solve 194a^2025-26

Question

Simplify the expression

4850 a^{2} - 26

Evaluate

194 a^{2} \times 25 - 26

Solution

4850 a^{2} - 26

Show Solution

2 (2425 a^{2} - 13)

Evaluate

194 a^{2} \times 25 - 26

Multiply the terms

4850 a^{2} - 26

Solution

2 (2425 a^{2} - 13)

Show Solution

a_{1} = - \frac{1261}{485}, a_{2} = \frac{1261}{485}

Alternative Form

a_{1} \approx - 0.073218, a_{2} \approx 0.073218

Evaluate

194 a^{2} \times 25 - 26

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

194 a^{2} \times 25 - 26 = 0

Multiply the terms

4850 a^{2} - 26 = 0

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

4850 a^{2} = 0 + 26

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

4850 a^{2} = 26

Divide both sides

\frac{4850 a ^{2}}{4850} = \frac{26}{4850}

Divide the numbers

a^{2} = \frac{26}{4850}

Cancel out the common factor 2

a^{2} = \frac{13}{2425}

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

a = \pm \frac{13}{2425}

Simplify the expression

More Steps

Evaluate

\frac{13}{2425}

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

\frac{13}{2425}

Simplify the radical expression

More Steps

Evaluate

2425

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 97

Write the number in exponential form with the base of 5

5^{2} \times 97

The root of a product is equal to the product of the roots of each factor

5^{2} \times 97

Reduce the index of the radical and exponent with 2

597

\frac{13}{5 97}

Multiply by the Conjugate

\frac{13 \times 97}{5 97 \times 97}

Multiply the numbers

More Steps

Evaluate

13 \times 97

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

13 \times 97

Calculate the product

1261

\frac{1261}{5 97 \times 97}

Multiply the numbers

More Steps

Evaluate

597 \times 97

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

5 \times 97

Multiply the terms

485

\frac{1261}{485}

a = \pm \frac{1261}{485}

Separate the equation into 2 possible cases

a = \frac{1261}{485} a = - \frac{1261}{485}

Solution

a_{1} = - \frac{1261}{485}, a_{2} = \frac{1261}{485}

Alternative Form

a_{1} \approx - 0.073218, a_{2} \approx 0.073218

Show Solution