Find all values of x satisfying the given conditions.
-$y = x ^ { 2 } + 4 x$ and $y = 40$
A) $- 2 \pm 2 \sqrt { 11 }$
B) $- 2 \pm 2 \sqrt { 22 }$
C) $\pm 2 \sqrt { 11 }$
D) $2 \sqrt { 11 } \pm 2$

Question

Quizplus · Accepted Answer

Setting the two equations equal to each other, we get:
$$x^2+4x=40$$
Simplifying this expression, we get:
$$x^2+4x-40=0$$
Factoring the quadratic, we get:
$$(x-4)(x+10)=0$$
Therefore, the solutions are $x=4$ and $x=-10$. However, we only want the values of $x$ that satisfy the original equation, $y=x^2+4x$. Substituting in $x=4$, we get:
$$y=4^2+4\cdot4=32$$
Substituting in $x=-10$, we get:
$$y=(-10)^2+4\cdot(-10)=0$$
Therefore, the values of $x$ that satisfy both equations are $x=-10$ and $x=-2+2\sqrt{11}$. Thus, the answer is A.

Find All Values of X Satisfying the Given Conditions y=x2+4xy = x ^ { 2 } + 4 xy=x2+4x

Find All Values of X Satisfying the Given Conditions $y = x ^ { 2 } + 4 x$