Solve for x (x^2)/4-(7x)/2+10=0

$\frac{x^{2}}{4} - \frac{7 x}{2} + 10 = 0$

Multiply each term in $\frac{x^{2}}{4} - \frac{7 x}{2} + 10 = 0$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{x^{2}}{4} - \frac{7 x}{2} + 10 = 0$ by $4$ .

$\frac{x^{2}}{4} \cdot 4 - \frac{7 x}{2} \cdot 4 + 10 \cdot 4 = 0 \cdot 4$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x^{2}}{4} \cdot 4 - \frac{7 x}{2} \cdot 4 + 10 \cdot 4 = 0 \cdot 4$

Rewrite the expression.

$x^{2} - \frac{7 x}{2} \cdot 4 + 10 \cdot 4 = 0 \cdot 4$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$x^{2} + \frac{- 7 x}{2} \cdot 4 + 10 \cdot 4 = 0 \cdot 4$

Factor $2$ out of $4$ .

$x^{2} + \frac{- 7 x}{2} \cdot (2 (2)) + 10 \cdot 4 = 0 \cdot 4$

Cancel the common factor.

$x^{2} + \frac{- 7 x}{2} \cdot (2 \cdot 2) + 10 \cdot 4 = 0 \cdot 4$

Rewrite the expression.

$x^{2} - 7 x \cdot 2 + 10 \cdot 4 = 0 \cdot 4$

Multiply $2$ by $- 7$ .

$x^{2} - 14 x + 10 \cdot 4 = 0 \cdot 4$

Multiply $10$ by $4$ .

$x^{2} - 14 x + 40 = 0 \cdot 4$

Simplify the right side.

Multiply $0$ by $4$ .

$x^{2} - 14 x + 40 = 0$

Factor $x^{2} - 14 x + 40$ 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 $40$ and whose sum is $- 14$ .

$- 10, - 4$

Write the factored form using these integers.

$(x - 10) (x - 4) = 0$

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

$x - 10 = 0$

$x - 4 = 0$

Set $x - 10$ equal to $0$ and solve for $x$ .

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

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.

$x = 4$

The final solution is all the values that make $(x - 10) (x - 4) = 0$ true.

$x = 10, 4$

Solve for x (x^2)/4-(7x)/2+10=0

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