How do you solve $7x^2=-21$ ?

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Answer 1 · 2017-05-25T01:01:04

See a solution process below:

First, divide each side of the equation by $color(red)(7)$ to isolate the $x^2$ term while keeping the equation balanced:

$(7x^2)/color(red)(7) = -21/color(red)(7)$

$(color(red)(cancel(color(black)(7)))x^2)/cancel(color(red)(7)) = -3$

$x^2 = -3$

Next, we would take the square root of each side of the equation to solve for $x$ while keeping the equation balanced.

However, there is no Real solution for the square root of a negative number, in this case the $sqrt(-3)$

Therefore, there is no real solution or the solution set is the empty or null set: ${O/}$

Answer 2 · 2017-05-25T01:04:40

No real solutions but rather, two complex solution : $x=isqrt3,x=-isqrt3$

Divide $7$ to both sides;

$cancel(7/7)x^2=-21/7$

$x^2=-3$

$sqrt(x^2)=sqrt(-3$ (Apply the square root property)

$x=+-sqrt(-3)$

There are no "real solutions" since the number inside the radical is negative but there are two "complex" solutions:

We can rewrite the expression above as:

$x=sqrt(-1)*sqrt3, x=-sqrt(-1)*sqrt3$

*Recall that $sqrt-1=i$

Therefore we can simplify the expression as:

$x=isqrt3,x=-isqrt3$ (This is our final answer)

How do you solve 7x^2=-217x^2=-21?