Solve 7074a^2-50 - ScanMath

Question

Factor the expression

2 (3537 a^{2} - 25)

Evaluate

7074 a^{2} - 50

Solution

2 (3537 a^{2} - 25)

Show Solution

a_{1} = - \frac{5 393}{1179}, a_{2} = \frac{5 393}{1179}

Alternative Form

a_{1} \approx - 0.084072, a_{2} \approx 0.084072

Evaluate

7074 a^{2} - 50

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

7074 a^{2} - 50 = 0

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

7074 a^{2} = 0 + 50

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

7074 a^{2} = 50

Divide both sides

\frac{7074 a ^{2}}{7074} = \frac{50}{7074}

Divide the numbers

a^{2} = \frac{50}{7074}

Cancel out the common factor 2

a^{2} = \frac{25}{3537}

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

a = \pm \frac{25}{3537}

Simplify the expression

More Steps

Evaluate

\frac{25}{3537}

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

\frac{25}{3537}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{3537}

Simplify the radical expression

More Steps

Evaluate

3537

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

9 \times 393

Write the number in exponential form with the base of 3

3^{2} \times 393

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

3^{2} \times 393

Reduce the index of the radical and exponent with 2

3393

\frac{5}{3 393}

Multiply by the Conjugate

\frac{5 393}{3 393 \times 393}

Multiply the numbers

More Steps

Evaluate

3393 \times 393

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

3 \times 393

Multiply the terms

1179

\frac{5 393}{1179}

a = \pm \frac{5 393}{1179}

Separate the equation into 2 possible cases

a = \frac{5 393}{1179} a = - \frac{5 393}{1179}

Solution

a_{1} = - \frac{5 393}{1179}, a_{2} = \frac{5 393}{1179}

Alternative Form

a_{1} \approx - 0.084072, a_{2} \approx 0.084072

Show Solution