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Solve the quadratic equation using your choice of the methods we learned in this module. Indicate which method you are using, and show your work.

[tex]\[ 4x^2 - 22 = x^2 + 5 \][/tex]

Sagot :

GinnyAnsweridn
Certainly! We'll solve the quadratic equation step-by-step. The equation is:

[tex]\[ 4x^2 - 22 = x^2 + 5 \][/tex]

### Step 1: Simplify the Equation
First, we need to move all the terms to one side to set the equation to zero.

[tex]\[ 4x^2 - 22 - x^2 - 5 = 0 \][/tex]

Combine like terms:

[tex]\[ (4x^2 - x^2) - 22 - 5 = 0 \][/tex]
[tex]\[ 3x^2 - 27 = 0 \][/tex]

### Step 2: Solve for [tex]\( x \)[/tex]
Now we have a simplified quadratic equation:

[tex]\[ 3x^2 - 27 = 0 \][/tex]

Add 27 to both sides:

[tex]\[ 3x^2 = 27 \][/tex]

Divide both sides by 3:

[tex]\[ x^2 = 9 \][/tex]

### Step 3: Find the Values of [tex]\( x \)[/tex]
To solve [tex]\( x^2 = 9 \)[/tex], take the square root of both sides:

[tex]\[ x = \pm \sqrt{9} \][/tex]
[tex]\[ x = \pm 3 \][/tex]

### Solution
The solutions to the quadratic equation [tex]\( 4x^2 - 22 = x^2 + 5 \)[/tex] are:

[tex]\[ x = 3 \; \text{and} \; x = -3 \][/tex]

These are the values of [tex]\( x \)[/tex] that satisfy the equation.
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