Finite Math Examples

$16 x^{2} = 56 x - 49$

Step 1

Subtract $56 x$ from both sides of the equation.

$16 x^{2} - 56 x = - 49$

Step 2

Add $49$ to both sides of the equation.

$16 x^{2} - 56 x + 49 = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

${(4 x)}^{2} - 56 x + 49 = 0$

Step 3.2

Rewrite $49$ as $7^{2}$ .

${(4 x)}^{2} - 56 x + 7^{2} = 0$

Step 3.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$56 x = 2 \cdot (4 x) \cdot 7$

Step 3.4

Rewrite the polynomial.

${(4 x)}^{2} - 2 \cdot (4 x) \cdot 7 + 7^{2} = 0$

Step 3.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 4 x$ and $b = 7$ .

${(4 x - 7)}^{2} = 0$

Step 4

Set the $4 x - 7$ equal to $0$ .

$4 x - 7 = 0$

Step 5

Solve for $x$ .

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Step 5.1

Add $7$ to both sides of the equation.

$4 x = 7$

Step 5.2

Divide each term in $4 x = 7$ by $4$ and simplify.

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Step 5.2.1

Divide each term in $4 x = 7$ by $4$ .

$\frac{4 x}{4} = \frac{7}{4}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{7}{4}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{4}$

Decimal Form:

$x = 1.75$

Mixed Number Form:

$x = 1 \frac{3}{4}$