Solve (25y)(5y - 2) - (4y -1)

Question

Simplify the expression

125 y^{2} - 54 y + 1

Show Solution

Find the roots

y_{1} = \frac{27 - 2 151}{125}, y_{2} = \frac{27 + 2 151}{125}

Alternative Form

y_{1} \approx 0.019389, y_{2} \approx 0.412611

Evaluate

(25 y) (5 y - 2) - (4 y - 1)

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

(25 y) (5 y - 2) - (4 y - 1) = 0

Multiply the terms

25 y (5 y - 2) - (4 y - 1) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

25 y (5 y - 2) - 4 y + 1 = 0

Calculate the sum or difference

More Steps

125 y^{2} - 54 y + 1 = 0

Substitute a= 125,b= - 54 and c= 1 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{54 \pm ( - 54 ) ^{2} - 4 \times 125}{2 \times 125}

Simplify the expression

y = \frac{54 \pm ( - 54 ) ^{2} - 4 \times 125}{250}

Simplify the expression

More Steps

y = \frac{54 \pm 2416}{250}

Simplify the radical expression

More Steps

y = \frac{54 \pm 4 151}{250}

Separate the equation into 2 possible cases

y = \frac{54 + 4 151}{250} y = \frac{54 - 4 151}{250}

Simplify the expression

More Steps

y = \frac{27 + 2 151}{125} y = \frac{54 - 4 151}{250}

Simplify the expression

More Steps

y = \frac{27 + 2 151}{125} y = \frac{27 - 2 151}{125}

Solution

y_{1} = \frac{27 - 2 151}{125}, y_{2} = \frac{27 + 2 151}{125}

Alternative Form

y_{1} \approx 0.019389, y_{2} \approx 0.412611

Show Solution