Solve 49q^4-4 - ScanMath

Question

Factor the expression

(7 q^{2} - 2) (7 q^{2} + 2)

Evaluate

49 q^{4} - 4

Rewrite the expression in exponential form

(7 q^{2})^{2} - 2^{2}

Solution

(7 q^{2} - 2) (7 q^{2} + 2)

Show Solution

q_{1} = - \frac{14}{7}, q_{2} = \frac{14}{7}

Alternative Form

q_{1} \approx - 0.534522, q_{2} \approx 0.534522

Evaluate

49 q^{4} - 4

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

49 q^{4} - 4 = 0

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

49 q^{4} = 0 + 4

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

49 q^{4} = 4

Divide both sides

\frac{49 q ^{4}}{49} = \frac{4}{49}

Divide the numbers

q^{4} = \frac{4}{49}

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

q = \pm 4 \frac{4}{49}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{49}

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

\frac{4 4}{4 49}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 49}

Simplify the radical expression

More Steps

Evaluate

449

Write the number in exponential form with the base of 7

4 7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{2}{7}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

2 \times 7

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

2 \times 7

Calculate the product

14

\frac{14}{7 \times 7}

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

\frac{14}{7}

q = \pm \frac{14}{7}

Separate the equation into 2 possible cases

q = \frac{14}{7} q = - \frac{14}{7}

Solution

q_{1} = - \frac{14}{7}, q_{2} = \frac{14}{7}

Alternative Form

q_{1} \approx - 0.534522, q_{2} \approx 0.534522

Show Solution