4 square root x-2+2=x+3
you need to use ( ). I don't know what is in the sqrt.
Solve this by getting the sqrt( ) on one side, constants on other side, then square both sides.
its 4(x-2+2)=x+3
4(x-2+2)=x+3
4x = x + 3
3x = 3
x = 1
To solve the equation, we need to isolate the variable 'x' on one side of the equation. Let's go step by step:
1. Start by subtracting 2 from both sides of the equation:
4√(x - 2) + 2 - 2 = x + 3 - 2
4√(x - 2) = x + 1
2. Next, divide both sides of the equation by 4:
(4√(x - 2))/4 = (x + 1)/4
√(x - 2) = (x + 1)/4
3. Now, square both sides of the equation:
(√(x - 2))^2 = ((x + 1)/4)^2
x - 2 = (x + 1)^2 / 16
4. Simplify the right side of the equation by squaring the numerator:
x - 2 = (x + 1)(x + 1) / 16
x - 2 = (x^2 + 2x + 1) / 16
5. Multiply both sides of the equation by 16 to get rid of the denominator:
16(x - 2) = x^2 + 2x + 1
6. Distribute 16 on the left side:
16x - 32 = x^2 + 2x + 1
7. Rearrange the equation to make it a quadratic equation:
0 = x^2 + 2x + 1 - 16x + 32
0 = x^2 - 14x + 33
Now, you can solve this quadratic equation using factoring, completing the square, or the quadratic formula.