Solve the system by any method, if possible. $x ^ { 2 } - 2 x = 7$
A) $x = 1 \pm 2 \sqrt { 2 }$
B) $16 i$
C) $- 36 i$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question

Quizplus · Accepted Answer

To solve the equation $x^2 - 2x = 7$, we first move all terms to one side to set the equation to 0: $x^2 - 2x - 7 = 0$. This is a quadratic equation, which can be solved using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -2$, and $c = -7$. Plugging these values into the formula gives $x = \frac{2 \pm \sqrt{(-2)^2 - 4(1)(-7)}}{2(1)} = \frac{2 \pm \sqrt{4 + 28}}{2} = \frac{2 \pm \sqrt{32}}{2} = \frac{2 \pm 4\sqrt{2}}{2} = 1 \pm 2\sqrt{2}$, which matches choice A.

Solve the System by Any Method, If Possible x2−2x=7x ^ { 2 } - 2 x = 7x2−2x=7

Solve the System by Any Method, If Possible $x ^ { 2 } - 2 x = 7$