To solve the equation 3x + 5 = x√7, we need to isolate x.
1. Start by subtracting x from both sides of the equation to get rid of x on the right side:
3x - x + 5 = x√7 - x
Simplified: 2x + 5 = x√7
2. Next, subtract 5 from both sides of the equation to isolate x:
2x + 5 - 5 = x√7 - 5
Simplified: 2x = x√7 - 5
3. To eliminate the square root on the right side, square both sides of the equation:
(2x)^2 = (x√7 - 5)^2
Simplified: 4x^2 = (x√7 - 5)(x√7 - 5)
4. Expand the right side of the equation using the foil method:
4x^2 = (x^2√7 - 5x√7 - 5x√7 + 25)
Simplified: 4x^2 = x^2√7 - 10x√7 + 25
5. Combine like terms on the right side of the equation:
4x^2 = x^2√7 - 20x√7 + 25
6. Move all terms to one side to set the equation equal to zero:
4x^2 - x^2√7 + 20x√7 - 25 = 0
Now you have a quadratic equation that can be solved using various methods like factoring, completing the square, or using the quadratic formula.