Solve 6p^42-76 - ScanMath

Question

Simplify the expression

12 p^{4} - 76

Evaluate

6 p^{4} \times 2 - 76

Solution

12 p^{4} - 76

Show Solution

4 (3 p^{4} - 19)

Evaluate

6 p^{4} \times 2 - 76

Multiply the terms

12 p^{4} - 76

Solution

4 (3 p^{4} - 19)

Show Solution

p_{1} = - \frac{4 513}{3}, p_{2} = \frac{4 513}{3}

Alternative Form

p_{1} \approx - 1.586383, p_{2} \approx 1.586383

Evaluate

6 p^{4} \times 2 - 76

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

6 p^{4} \times 2 - 76 = 0

Multiply the terms

12 p^{4} - 76 = 0

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

12 p^{4} = 0 + 76

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

12 p^{4} = 76

Divide both sides

\frac{12 p ^{4}}{12} = \frac{76}{12}

Divide the numbers

p^{4} = \frac{76}{12}

Cancel out the common factor 4

p^{4} = \frac{19}{3}

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

p = \pm 4 \frac{19}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{19}{3}

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

\frac{4 19}{4 3}

Multiply by the Conjugate

\frac{4 19 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 19 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

419 \times 427

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

4 19 \times 27

Calculate the product

4513

\frac{4 513}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 513}{3}

p = \pm \frac{4 513}{3}

Separate the equation into 2 possible cases

p = \frac{4 513}{3} p = - \frac{4 513}{3}

Solution

p_{1} = - \frac{4 513}{3}, p_{2} = \frac{4 513}{3}

Alternative Form

p_{1} \approx - 1.586383, p_{2} \approx 1.586383

Show Solution