Solve 25x^2-6036 - ScanMath

Question

Find the roots

x_{1} = - \frac{2 1509}{5}, x_{2} = \frac{2 1509}{5}

Alternative Form

x_{1} \approx - 15.53834, x_{2} \approx 15.53834

Evaluate

25 x^{2} - 6036

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

25 x^{2} - 6036 = 0

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

25 x^{2} = 0 + 6036

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

25 x^{2} = 6036

Divide both sides

\frac{25 x ^{2}}{25} = \frac{6036}{25}

Divide the numbers

x^{2} = \frac{6036}{25}

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

x = \pm \frac{6036}{25}

Simplify the expression

More Steps

Evaluate

\frac{6036}{25}

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

\frac{6036}{25}

Simplify the radical expression

More Steps

Evaluate

6036

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

4 \times 1509

Write the number in exponential form with the base of 2

2^{2} \times 1509

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

2^{2} \times 1509

Reduce the index of the radical and exponent with 2

21509

\frac{2 1509}{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 1509}{5}

x = \pm \frac{2 1509}{5}

Separate the equation into 2 possible cases

x = \frac{2 1509}{5} x = - \frac{2 1509}{5}

Solution

x_{1} = - \frac{2 1509}{5}, x_{2} = \frac{2 1509}{5}

Alternative Form

x_{1} \approx - 15.53834, x_{2} \approx 15.53834

Show Solution