Solve for x (x^2)/4-(5x)/2+6=0

$\frac{x^{2}}{4} - \frac{5 x}{2} + 6 = 0$

Step 1

Multiply each term in $\frac{x^{2}}{4} - \frac{5 x}{2} + 6 = 0$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{x^{2}}{4} - \frac{5 x}{2} + 6 = 0$ by $4$ .

$\frac{x^{2}}{4} \cdot 4 - \frac{5 x}{2} \cdot 4 + 6 \cdot 4 = 0 \cdot 4$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x^{2}}{4} \cdot 4 - \frac{5 x}{2} \cdot 4 + 6 \cdot 4 = 0 \cdot 4$

Rewrite the expression.

$x^{2} - \frac{5 x}{2} \cdot 4 + 6 \cdot 4 = 0 \cdot 4$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$x^{2} + \frac{- 5 x}{2} \cdot 4 + 6 \cdot 4 = 0 \cdot 4$

Factor $2$ out of $4$ .

$x^{2} + \frac{- 5 x}{2} \cdot (2 (2)) + 6 \cdot 4 = 0 \cdot 4$

Cancel the common factor.

$x^{2} + \frac{- 5 x}{2} \cdot (2 \cdot 2) + 6 \cdot 4 = 0 \cdot 4$

Rewrite the expression.

$x^{2} - 5 x \cdot 2 + 6 \cdot 4 = 0 \cdot 4$

Multiply $2$ by $- 5$ .

$x^{2} - 10 x + 6 \cdot 4 = 0 \cdot 4$

Multiply $6$ by $4$ .

$x^{2} - 10 x + 24 = 0 \cdot 4$

Simplify the right side.

Multiply $0$ by $4$ .

$x^{2} - 10 x + 24 = 0$

Step 2

Factor $x^{2} - 10 x + 24$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $24$ and whose sum is $- 10$ .

$- 6, - 4$

Write the factored form using these integers.

$(x - 6) (x - 4) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 6 = 0$

$x - 4 = 0$

Step 4

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 5

Set $x - 4$ equal to $0$ and solve for $x$ .

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 6

The final solution is all the values that make $(x - 6) (x - 4) = 0$ true.

$x = 6, 4$

Solve for x (x^2)/4-(5x)/2+6=0

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