Solve 250y^2-90 - ScanMath

Question

Factor the expression

10 (5 y - 3) (5 y + 3)

Evaluate

250 y^{2} - 90

Factor out 10 from the expression

10 (25 y^{2} - 9)

Solution

More Steps

Evaluate

25 y^{2} - 9

Rewrite the expression in exponential form

(5 y)^{2} - 3^{2}

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

(5 y - 3) (5 y + 3)

10 (5 y - 3) (5 y + 3)

Show Solution

y_{1} = - \frac{3}{5}, y_{2} = \frac{3}{5}

Alternative Form

y_{1} = - 0.6, y_{2} = 0.6

Evaluate

250 y^{2} - 90

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

250 y^{2} - 90 = 0

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

250 y^{2} = 0 + 90

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

250 y^{2} = 90

Divide both sides

\frac{250 y ^{2}}{250} = \frac{90}{250}

Divide the numbers

y^{2} = \frac{90}{250}

Cancel out the common factor 10

y^{2} = \frac{9}{25}

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

y = \pm \frac{9}{25}

Simplify the expression

More Steps

Evaluate

\frac{9}{25}

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

\frac{9}{25}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{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{3}{5}

y = \pm \frac{3}{5}

Separate the equation into 2 possible cases

y = \frac{3}{5} y = - \frac{3}{5}

Solution

y_{1} = - \frac{3}{5}, y_{2} = \frac{3}{5}

Alternative Form

y_{1} = - 0.6, y_{2} = 0.6

Show Solution