Solve this equation:
√4x+8=6
If there is more then one solution enter with a comma
√4x+8=6
since √4x >= 0, there is no solution.
Now, if you meant
√(4x+8)=6
4x+8 = 36
4x = 28
x = 7
To solve the equation √(4x+8) = 6, you can follow these steps:
Step 1: Square both sides of the equation to eliminate the square root: (√(4x+8))^2 = 6^2.
Simplifying this gives us:
4x + 8 = 36.
Step 2: Subtract 8 from both sides of the equation to isolate the term with x: 4x = 36 - 8.
Simplifying further gives us:
4x = 28.
Step 3: Divide both sides of the equation by 4 to solve for x: 4x/4 = 28/4.
Simplifying this gives us:
x = 7.
So the solution to the equation √(4x+8) = 6 is x = 7.
To solve the equation √(4x+8) = 6, follow these steps:
Step 1: Isolate the square root term.
Subtract 8 from both sides of the equation:
√(4x+8) - 8 = 6 - 8
√(4x+8) - 8 = -2
Step 2: Eliminate the square root.
Square both sides of the equation:
(√(4x+8) - 8)^2 = (-2)^2
(4x+8) - 16√(4x+8) + 64 = 4
4x + 8 - 16√(4x+8) + 64 = 4
4x + 72 - 16√(4x+8) = 4
Step 3: Simplify and solve the resulting equation.
Move the constant term to the other side of the equation:
4x - 16√(4x+8) = -68
Step 4: Solve for √(4x+8).
Isolate the square root term:
-16√(4x+8) = -68 - 4x
Square both sides of the equation:
(-16√(4x+8))^2 = (-68 - 4x)^2
256(4x+8) = (68 + 4x)^2
1024x + 2048 = 4624 + 544x + 16x^2
Rearrange the equation and simplify:
16x^2 + (544 - 1024)x + (4624 - 2048) = 0
16x^2 - 480x + 2576 = 0
Step 5: Solve the quadratic equation.
Use factoring, completing the square, or the quadratic formula to obtain the solutions.
In this case, the quadratic equation does not factor nicely, so we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from the quadratic equation:
x = (-(-480) ± √((-480)^2 - 4(16)(2576))) / (2(16))
x = (480 ± √(230,400 - 164,864)) / 32
x = (480 ± √65,536) / 32
x = (480 ± 256) / 32
Simplifying further:
For the positive square root:
x = (480 + 256) / 32
x = 736 / 32
x = 23.
For the negative square root:
x = (480 - 256) / 32
x = 224 / 32
x = 7.
Therefore, the solutions to the equation √(4x+8) = 6 are x = 23 and x = 7.