Solve (25:53)*x^2-4

Question

Simplify the expression

\frac{25}{53} x^{2} - 4

Evaluate

(25 \div 53) x^{2} - 4

Solution

\frac{25}{53} x^{2} - 4

Show Solution

\frac{1}{53} (25 x^{2} - 212)

Evaluate

(25 \div 53) x^{2} - 4

Rewrite the expression

\frac{25}{53} x^{2} - 4

Solution

\frac{1}{53} (25 x^{2} - 212)

Show Solution

x_{1} = - \frac{2 53}{5}, x_{2} = \frac{2 53}{5}

Alternative Form

x_{1} \approx - 2.912044, x_{2} \approx 2.912044

Evaluate

(25 \div 53) x^{2} - 4

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

(25 \div 53) x^{2} - 4 = 0

Rewrite the expression

\frac{25}{53} x^{2} - 4 = 0

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

\frac{25}{53} x^{2} = 0 + 4

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

\frac{25}{53} x^{2} = 4

Multiply by the reciprocal

\frac{25}{53} x^{2} \times \frac{53}{25} = 4 \times \frac{53}{25}

Multiply

x^{2} = 4 \times \frac{53}{25}

Multiply

More Steps

Evaluate

4 \times \frac{53}{25}

Multiply the numbers

\frac{4 \times 53}{25}

Multiply the numbers

\frac{212}{25}

x^{2} = \frac{212}{25}

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

x = \pm \frac{212}{25}

Simplify the expression

More Steps

Evaluate

\frac{212}{25}

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

\frac{212}{25}

Simplify the radical expression

More Steps

Evaluate

212

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

4 \times 53

Write the number in exponential form with the base of 2

2^{2} \times 53

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

2^{2} \times 53

Reduce the index of the radical and exponent with 2

253

\frac{2 53}{25}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{2 53}{5}

x = \pm \frac{2 53}{5}

Separate the equation into 2 possible cases

x = \frac{2 53}{5} x = - \frac{2 53}{5}

Solution

x_{1} = - \frac{2 53}{5}, x_{2} = \frac{2 53}{5}

Alternative Form

x_{1} \approx - 2.912044, x_{2} \approx 2.912044

Show Solution