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.
