Solve 36a^2-49=(6a-7)(6a 7)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

a_{1} = \frac{7}{36}, a_{2} = \frac{7}{6}

Alternative Form

a_{1} = 0.19 \dot{4}, a_{2} = 1.1 \dot{6}

Evaluate

36 a^{2} - 49 = (6 a - 7) (6 a \times 7)

Remove the parentheses

36 a^{2} - 49 = (6 a - 7) \times 6 a \times 7

Multiply the terms

More Steps

Evaluate

(6 a - 7) \times 6 a \times 7

Multiply the terms

(6 a - 7) \times 42 a

Multiply the terms

42 a (6 a - 7)

36 a^{2} - 49 = 42 a (6 a - 7)

Expand the expression

More Steps

Evaluate

42 a (6 a - 7)

Apply the distributive property

42 a \times 6 a - 42 a \times 7

Multiply the terms

More Steps

Evaluate

42 a \times 6 a

Multiply the numbers

252 a \times a

Multiply the terms

252 a^{2}

252 a^{2} - 42 a \times 7

Multiply the numbers

252 a^{2} - 294 a

36 a^{2} - 49 = 252 a^{2} - 294 a

Move the expression to the left side

- 216 a^{2} - 49 + 294 a = 0

Factor the expression

More Steps

Evaluate

- 216 a^{2} - 49 + 294 a

Reorder the terms

- 216 a^{2} + 294 a - 49

Rewrite the expression

- 216 a^{2} + (42 + 252) a - 49

Calculate

- 216 a^{2} + 42 a + 252 a - 49

Rewrite the expression

- 6 a \times 36 a + 6 a \times 7 + 7 \times 36 a - 7 \times 7

Factor out - 6 a from the expression

- 6 a (36 a - 7) + 7 \times 36 a - 7 \times 7

Factor out 7 from the expression

- 6 a (36 a - 7) + 7 (36 a - 7)

Factor out 36 a - 7 from the expression

(- 6 a + 7) (36 a - 7)

(- 6 a + 7) (36 a - 7) = 0

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

- 6 a + 7 = 0 36 a - 7 = 0

Solve the equation for a

More Steps

Evaluate

- 6 a + 7 = 0

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

- 6 a = 0 - 7

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

- 6 a = - 7

Change the signs on both sides of the equation

6 a = 7

Divide both sides

\frac{6 a}{6} = \frac{7}{6}

Divide the numbers

a = \frac{7}{6}

a = \frac{7}{6} 36 a - 7 = 0

Solve the equation for a

More Steps

Evaluate

36 a - 7 = 0

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

36 a = 0 + 7

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

36 a = 7

Divide both sides

\frac{36 a}{36} = \frac{7}{36}

Divide the numbers

a = \frac{7}{36}

a = \frac{7}{6} a = \frac{7}{36}

Solution

a_{1} = \frac{7}{36}, a_{2} = \frac{7}{6}

Alternative Form

a_{1} = 0.19 \dot{4}, a_{2} = 1.1 \dot{6}

Show Solution

Solve the quadratic equation

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