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Solve the following quadratic equation:
[tex]\[ 4x^2 - 10 = 186 \][/tex]

A. [tex]\( x = -6 \)[/tex] and [tex]\( x = 6 \)[/tex]
B. [tex]\( x = -10 \)[/tex] and [tex]\( x = 10 \)[/tex]
C. [tex]\( x = -7 \)[/tex] and [tex]\( x = 7 \)[/tex]
D. [tex]\( x = -4 \)[/tex] and [tex]\( x = 4 \)[/tex]

Sagot :

GinnyAnswer
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]
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