Solve (7x^23-8)^2

Question

Simplify the expression

441 x^{4} - 336 x^{2} + 64

Evaluate

(7 x^{2} \times 3 - 8)^{2}

Multiply the terms

(21 x^{2} - 8)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(21 x^{2})^{2} - 2 \times 21 x^{2} \times 8 + 8^{2}

Solution

441 x^{4} - 336 x^{2} + 64

Show Solution

x_{1} = - \frac{2 42}{21}, x_{2} = \frac{2 42}{21}

Alternative Form

x_{1} \approx - 0.617213, x_{2} \approx 0.617213

Evaluate

(7 x^{2} \times 3 - 8)^{2}

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

(7 x^{2} \times 3 - 8)^{2} = 0

Multiply the terms

(21 x^{2} - 8)^{2} = 0

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

21 x^{2} - 8 = 0

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

21 x^{2} = 0 + 8

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

21 x^{2} = 8

Divide both sides

\frac{21 x ^{2}}{21} = \frac{8}{21}

Divide the numbers

x^{2} = \frac{8}{21}

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

x = \pm \frac{8}{21}

Simplify the expression

More Steps

Evaluate

\frac{8}{21}

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

\frac{8}{21}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{2 2}{21}

Multiply by the Conjugate

\frac{2 2 \times 21}{21 \times 21}

Multiply the numbers

More Steps

Evaluate

2 \times 21

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

2 \times 21

Calculate the product

42

\frac{2 42}{21 \times 21}

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

\frac{2 42}{21}

x = \pm \frac{2 42}{21}

Separate the equation into 2 possible cases

x = \frac{2 42}{21} x = - \frac{2 42}{21}

Solution

x_{1} = - \frac{2 42}{21}, x_{2} = \frac{2 42}{21}

Alternative Form

x_{1} \approx - 0.617213, x_{2} \approx 0.617213

Show Solution