Solve 38 (5b^22)=7b^45

Question

Solve the equation

b_{1} = - \frac{2 133}{7}, b_{2} = 0, b_{3} = \frac{2 133}{7}

Alternative Form

b_{1} \approx - 3.295018, b_{2} = 0, b_{3} \approx 3.295018

Evaluate

38 (5 b^{2} \times 2) = 7 b^{4} \times 5

Remove the parentheses

38 \times 5 b^{2} \times 2 = 7 b^{4} \times 5

Simplify

38 b^{2} \times 2 = 7 b^{4}

Multiply the terms

76 b^{2} = 7 b^{4}

Add or subtract both sides

76 b^{2} - 7 b^{4} = 0

Factor the expression

b^{2} (76 - 7 b^{2}) = 0

Separate the equation into 2 possible cases

b^{2} = 0 76 - 7 b^{2} = 0

The only way a power can be 0 is when the base equals 0

b = 0 76 - 7 b^{2} = 0

Solve the equation

More Steps

Evaluate

76 - 7 b^{2} = 0

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

- 7 b^{2} = 0 - 76

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

- 7 b^{2} = - 76

Change the signs on both sides of the equation

7 b^{2} = 76

Divide both sides

\frac{7 b ^{2}}{7} = \frac{76}{7}

Divide the numbers

b^{2} = \frac{76}{7}

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

b = \pm \frac{76}{7}

Simplify the expression

More Steps

Evaluate

\frac{76}{7}

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

\frac{76}{7}

Simplify the radical expression

\frac{2 19}{7}

Multiply by the Conjugate

\frac{2 19 \times 7}{7 \times 7}

Multiply the numbers

\frac{2 133}{7 \times 7}

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

\frac{2 133}{7}

b = \pm \frac{2 133}{7}

Separate the equation into 2 possible cases

b = \frac{2 133}{7} b = - \frac{2 133}{7}

b = 0 b = \frac{2 133}{7} b = - \frac{2 133}{7}

Solution

b_{1} = - \frac{2 133}{7}, b_{2} = 0, b_{3} = \frac{2 133}{7}

Alternative Form

b_{1} \approx - 3.295018, b_{2} = 0, b_{3} \approx 3.295018

Show Solution