Sure, let's solve the given quadratic equation step-by-step:
The equation we have is:
[tex]\[ 4x^2 - 10 = 186 \][/tex]
Step 1: Isolate the quadratic term.
Add 10 to both sides of the equation to achieve this:
[tex]\[ 4x^2 - 10 + 10 = 186 + 10 \][/tex]
This simplifies to:
[tex]\[ 4x^2 = 196 \][/tex]
Step 2: Solve for [tex]\( x^2 \)[/tex].
Divide both sides by 4:
[tex]\[ \frac{4x^2}{4} = \frac{196}{4} \][/tex]
This simplifies to:
[tex]\[ x^2 = 49 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
Take the square root of both sides of the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \pm \sqrt{49} \][/tex]
This simplifies to:
[tex]\[ x = \pm 7 \][/tex]
Therefore, the solutions to the quadratic equation are [tex]\( x = -7 \)[/tex] and [tex]\( x = 7 \)[/tex].
So, the correct answer is:
[tex]\[ x = -7 \text{ and } 7 \][/tex]
