Solve by Factoring x^2-7x+4=0

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

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = - 7$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (1 \cdot 4)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 16}}{2 \cdot 1}$

Subtract $16$ from $49$ .

$x = \frac{7 \pm \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{33}}{2}$

Step 4

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 16}}{2 \cdot 1}$

Subtract $16$ from $49$ .

$x = \frac{7 \pm \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{33}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{7 + \sqrt{33}}{2}$

Step 5

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 16}}{2 \cdot 1}$

Subtract $16$ from $49$ .

$x = \frac{7 \pm \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{33}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{7 - \sqrt{33}}{2}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{7 + \sqrt{33}}{2}, \frac{7 - \sqrt{33}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 + \sqrt{33}}{2}, \frac{7 - \sqrt{33}}{2}$

Decimal Form:

$x = 6.37228132 \dots, 0.62771867 \dots$

Solve by Factoring x^2-7x+4=0

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