![$$x = 7 \quad \text{or} \quad x = 1$$](https://img.qammunity.org/2022/formulas/mathematics/middle-school/ttb2k4019n2xlc9ndeaph07tjw6mjpsvyc.png)
Let’s find the value of x in the equation:
![$$x^2-8x+7=0$$](https://img.qammunity.org/2022/formulas/mathematics/middle-school/drfrm914hq1xd6v9gvx5d5x4xlfh19e815.png)
We can solve the equation using the quadratic formula, which is a general formula for solving quadratic equations.
Steps to solve:
1. Use the quadratic formula:
![\[ x = (-b \pm √(b^2 - 4ac))/(2a) \]](https://img.qammunity.org/2022/formulas/mathematics/middle-school/dykbynok2shwklm89mcx36t77uhe9mijt1.png)
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -8, and c = 7. Substituting these values into the formula, we get:
![\[ x = (-(-8) \pm √((-8)^2 - 4(1)(7)))/(2(1)) \]](https://img.qammunity.org/2022/formulas/mathematics/middle-school/ylh5rdwzchy7sla2lik5jm7i0m1d4wjkfq.png)
![\[ x = (8 \pm √(32))/(2) \]](https://img.qammunity.org/2022/formulas/mathematics/middle-school/wbe5lfu98bue9v0a5653j3juvruikk2hr6.png)
![\[ x = (8 \pm 4√(2))/(2) \]](https://img.qammunity.org/2022/formulas/mathematics/middle-school/kowu19uvkef24ydh1l7wopdqr67bpwdoov.png)
2. Separate the solutions and simplify:
![$$x = 4 \pm 2√(2)$$](https://img.qammunity.org/2022/formulas/mathematics/middle-school/ct282anwlohbzd3ar08koso4wfu78yhh9p.png)
![$$x = 7 \text{ or } x = 1$$](https://img.qammunity.org/2022/formulas/mathematics/middle-school/8lenolmegip8g6r6pgf1ezkumpq570mq3l.png)