Finite Math Examples

$x^{2} {(x + 28)}^{2} = 52^{2}$

Step 1

Simplify $x^{2} {(x + 28)}^{2}$ .

Tap for more steps...

Step 1.1

Rewrite ${(x + 28)}^{2}$ as $(x + 28) (x + 28)$ .

$x^{2} ((x + 28) (x + 28)) = 52^{2}$

Step 1.2

Expand $(x + 28) (x + 28)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$x^{2} (x (x + 28) + 28 (x + 28)) = 52^{2}$

Step 1.2.2

Apply the distributive property.

$x^{2} (x \cdot x + x \cdot 28 + 28 (x + 28)) = 52^{2}$

Step 1.2.3

Apply the distributive property.

$x^{2} (x \cdot x + x \cdot 28 + 28 x + 28 \cdot 28) = 52^{2}$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

$x^{2} (x^{2} + x \cdot 28 + 28 x + 28 \cdot 28) = 52^{2}$

Step 1.3.1.2

Move $28$ to the left of $x$ .

$x^{2} (x^{2} + 28 \cdot x + 28 x + 28 \cdot 28) = 52^{2}$

Step 1.3.1.3

Multiply $28$ by $28$ .

$x^{2} (x^{2} + 28 x + 28 x + 784) = 52^{2}$

Step 1.3.2

Add $28 x$ and $28 x$ .

$x^{2} (x^{2} + 56 x + 784) = 52^{2}$

Step 1.4

Apply the distributive property.

$x^{2} x^{2} + x^{2} (56 x) + x^{2} \cdot 784 = 52^{2}$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 1.5.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 2} + x^{2} (56 x) + x^{2} \cdot 784 = 52^{2}$

Step 1.5.1.2

Add $2$ and $2$ .

$x^{4} + x^{2} (56 x) + x^{2} \cdot 784 = 52^{2}$

Step 1.5.2

Rewrite using the commutative property of multiplication.

$x^{4} + 56 x^{2} x + x^{2} \cdot 784 = 52^{2}$

Step 1.5.3

Move $784$ to the left of $x^{2}$ .

$x^{4} + 56 x^{2} x + 784 \cdot x^{2} = 52^{2}$

Step 1.6

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.6.1

Move $x$ .

$x^{4} + 56 (x \cdot x^{2}) + 784 \cdot x^{2} = 52^{2}$

Step 1.6.2

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 1.6.2.1

Raise $x$ to the power of $1$ .

$x^{4} + 56 (x^{1} x^{2}) + 784 \cdot x^{2} = 52^{2}$

Step 1.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} + 56 x^{1 + 2} + 784 \cdot x^{2} = 52^{2}$

Step 1.6.3

Add $1$ and $2$ .

$x^{4} + 56 x^{3} + 784 \cdot x^{2} = 52^{2}$

$x^{4} + 56 x^{3} + 784 x^{2} = 52^{2}$

Step 2

Raise $52$ to the power of $2$ .

$x^{4} + 56 x^{3} + 784 x^{2} = 2704$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 29.74801574, - 26, - 2, 1.74801574$

Step 4