Solve (2y-5)^2 - y^2=88

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - \frac{7}{3}, y_{2} = 9

Alternative Form

y_{1} = - 2. \dot{3}, y_{2} = 9

Evaluate

(2 y - 5)^{2} - y^{2} = 88

Expand the expression

More Steps

Evaluate

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

Expand the expression

More Steps

Evaluate

(2 y - 5)^{2}

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

(2 y)^{2} - 2 \times 2 y \times 5 + 5^{2}

Calculate

4 y^{2} - 20 y + 25

4 y^{2} - 20 y + 25 - y^{2}

Subtract the terms

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Evaluate

4 y^{2} - y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 1) y^{2}

Subtract the numbers

3 y^{2}

3 y^{2} - 20 y + 25

3 y^{2} - 20 y + 25 = 88

Move the expression to the left side

3 y^{2} - 20 y - 63 = 0

Factor the expression

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Evaluate

3 y^{2} - 20 y - 63

Rewrite the expression

3 y^{2} + (7 - 27) y - 63

Calculate

3 y^{2} + 7 y - 27 y - 63

Rewrite the expression

y \times 3 y + y \times 7 - 9 \times 3 y - 9 \times 7

Factor out y from the expression

y (3 y + 7) - 9 \times 3 y - 9 \times 7

Factor out - 9 from the expression

y (3 y + 7) - 9 (3 y + 7)

Factor out 3 y + 7 from the expression

(y - 9) (3 y + 7)

(y - 9) (3 y + 7) = 0

When the product of factors equals 0,at least one factor is 0

y - 9 = 0 3 y + 7 = 0

Solve the equation for y

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Evaluate

y - 9 = 0

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

y = 0 + 9

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

y = 9

y = 9 3 y + 7 = 0

Solve the equation for y

More Steps

Evaluate

3 y + 7 = 0

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

3 y = 0 - 7

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

3 y = - 7

Divide both sides

\frac{3 y}{3} = \frac{- 7}{3}

Divide the numbers

y = \frac{- 7}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y = - \frac{7}{3}

y = 9 y = - \frac{7}{3}

Solution

y_{1} = - \frac{7}{3}, y_{2} = 9

Alternative Form

y_{1} = - 2. \dot{3}, y_{2} = 9

Show Solution