Solve 16-50x^25x^(2)=0

Question

Solve the equation

x_{1} = - \frac{4 40}{5}, x_{2} = \frac{4 40}{5}

Alternative Form

x_{1} \approx - 0.502973, x_{2} \approx 0.502973

Evaluate

16 - 50 x^{2} \times 5 x^{2} = 0

Multiply

More Steps

Evaluate

50 x^{2} \times 5 x^{2}

Multiply the terms

250 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

250 x^{2 + 2}

Add the numbers

250 x^{4}

16 - 250 x^{4} = 0

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

- 250 x^{4} = 0 - 16

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

- 250 x^{4} = - 16

Change the signs on both sides of the equation

250 x^{4} = 16

Divide both sides

\frac{250 x ^{4}}{250} = \frac{16}{250}

Divide the numbers

x^{4} = \frac{16}{250}

Cancel out the common factor 2

x^{4} = \frac{8}{125}

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

x = \pm 4 \frac{8}{125}

Simplify the expression

More Steps

Evaluate

4 \frac{8}{125}

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

\frac{4 8}{4 125}

Multiply by the Conjugate

\frac{4 8 \times 4 12 5 ^{3}}{4 125 \times 4 12 5 ^{3}}

Simplify

\frac{4 8 \times 5 ^{2} 4 5}{4 125 \times 4 12 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 5^{2} 45

Multiply the terms

440 \times 5^{2}

Use the commutative property to reorder the terms

5^{2} 440

\frac{5 ^{2} 4 40}{4 125 \times 4 12 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

4125 \times 4 12 5^{3}

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

4 125 \times 12 5^{3}

Calculate the product

4 12 5^{4}

Transform the expression

4 5^{12}

Reduce the index of the radical and exponent with 4

5^{3}

\frac{5 ^{2} 4 40}{5 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{5 ^{2}}{5 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{5 ^{3 - 2}}

Subtract the terms

\frac{1}{5 ^{1}}

Simplify

\frac{1}{5}

\frac{4 40}{5}

x = \pm \frac{4 40}{5}

Separate the equation into 2 possible cases

x = \frac{4 40}{5} x = - \frac{4 40}{5}

Solution

x_{1} = - \frac{4 40}{5}, x_{2} = \frac{4 40}{5}

Alternative Form

x_{1} \approx - 0.502973, x_{2} \approx 0.502973

Show Solution