Question

topic 4: the number i
solve each equation. leave your answer in terms of i
$x^2 + 4 = -7$
$-10n^2 = 810$
$8v^2 = -168$
$m^2 + 7 = -10$
$a^2 - 1 = -12$
$-8x^2 = 64$
$(x - 4)^2 = -25$
$(x - 5)^2 = -16$

Explanation:

Solving \( x^2 + 4 = -7 \)

Step1: Isolate \( x^2 \)

Subtract 4 from both sides: \( x^2 = -7 - 4 \)
\( x^2 = -11 \)

Step2: Solve for \( x \)

Take square roots, use \( i = \sqrt{-1} \): \( x = \pm\sqrt{-11} = \pm i\sqrt{11} \)

Step1: Isolate \( n^2 \)

Divide both sides by -10: \( n^2 = \frac{810}{-10} \)
\( n^2 = -81 \)

Step2: Solve for \( n \)

Take square roots: \( n = \pm\sqrt{-81} = \pm 9i \)

Step1: Isolate \( v^2 \)

Divide both sides by 8: \( v^2 = \frac{-168}{8} \)
\( v^2 = -21 \)

Step2: Solve for \( v \)

Take square roots: \( v = \pm\sqrt{-21} = \pm i\sqrt{21} \)

Answer:

\( x = \pm i\sqrt{11} \)

Solving \( -10n^2 = 810 \)