Solve 9p^2-42p^49=0

Question

Solve the equation

p_{1} = - \frac{42}{42}, p_{2} = 0, p_{3} = \frac{42}{42}

Alternative Form

p_{1} \approx - 0.154303, p_{2} = 0, p_{3} \approx 0.154303

Evaluate

9 p^{2} - 42 p^{4} \times 9 = 0

Multiply the terms

9 p^{2} - 378 p^{4} = 0

Factor the expression

9 p^{2} (1 - 42 p^{2}) = 0

Divide both sides

p^{2} (1 - 42 p^{2}) = 0

Separate the equation into 2 possible cases

p^{2} = 0 1 - 42 p^{2} = 0

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

p = 0 1 - 42 p^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 42 p^{2} = 0

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

- 42 p^{2} = 0 - 1

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

- 42 p^{2} = - 1

Change the signs on both sides of the equation

42 p^{2} = 1

Divide both sides

\frac{42 p ^{2}}{42} = \frac{1}{42}

Divide the numbers

p^{2} = \frac{1}{42}

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

p = \pm \frac{1}{42}

Simplify the expression

More Steps

Evaluate

\frac{1}{42}

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

\frac{1}{42}

Simplify the radical expression

\frac{1}{42}

Multiply by the Conjugate

\frac{42}{42 \times 42}

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

\frac{42}{42}

p = \pm \frac{42}{42}

Separate the equation into 2 possible cases

p = \frac{42}{42} p = - \frac{42}{42}

p = 0 p = \frac{42}{42} p = - \frac{42}{42}

Solution

p_{1} = - \frac{42}{42}, p_{2} = 0, p_{3} = \frac{42}{42}

Alternative Form

p_{1} \approx - 0.154303, p_{2} = 0, p_{3} \approx 0.154303

Show Solution