square root of x+4-2square x-1=-1
could help me please.
do you mean
√(x+4) - 2√(x-1) = -1 ?
please confirm
Yes you are right it do not have a parentesis it has square root.
Ok, move it around a bit
√(x+4) + 1 = 2√(x-1)
square both sides
x+4 +2√(x+4) + 1 = 4(x-1)
2√(x+4) = 3x - 9
square again
4(x+4) = 9x^2 - 54x + 81
9x^2 - 58x + 65 = 0
(x-5)(9x - 13) = 0
x = 5 or x = 13/9
since we squared, both answers must be checked
if x=5
LS = √9 - 2√4 = -1 = RS
if x = 13
LS = √(49/9) - 2√(4/9)
= 7/3 - 4/3 = +1 ≠ RS
so x = 5
Of course, I can help you with that equation! Let's go step by step to find the solution.
The equation you provided is: √(x + 4) - 2√(x - 1) = -1.
Step 1: Isolate the radical terms.
To do this, we will move the -1 to the other side of the equation, getting rid of the constant term on the left side:
√(x + 4) - 2√(x - 1) + 1 = 0.
Step 2: Simplify the radicals.
There are two square roots in this equation, so let's work on simplifying them. Start with the first term: √(x + 4).
Since there are no like terms to combine with, it can't be simplified further.
Now let's simplify the second term: -2√(x - 1).
We can rewrite it as -2 * √(x - 1).
Step 3: Combine like terms.
Using the simplified expressions from Step 2, we have:
√(x + 4) - 2 * √(x - 1) + 1 = 0.
Step 4: Pick a variable to solve for.
In this case, we need to solve for x.
Step 5: Isolate the radical terms.
We need to isolate the radicals, so let's move the non-radical terms to the other side of the equation:
√(x + 4) - 2 * √(x - 1) = -1.
Step 6: Simplify the radicals (if possible).
Since there are no like terms to combine with, the radicals cannot be simplified further.
Step 7: Square both sides of the equation.
To eliminate the radicals, we need to square both sides of the equation:
(√(x + 4) - 2 * √(x - 1))^2 = (-1)^2.
Step 8: Expand and simplify.
Expanding the square on the left side gives us:
(x + 4) - 2 * (√(x + 4) * √(x - 1)) + 4 * (x - 1) = 1.
Simplifying further, we have:
x + 4 - 2√((x + 4)(x - 1)) + 4x - 4 = 1.
Combining like terms, we get:
5x - 2√((x + 4)(x - 1)) = 1.
Step 9: Isolate the radical term (if necessary).
Move the constant term to the other side of the equation:
5x - 1 = 2√((x + 4)(x - 1)).
Step 10: Square both sides of the equation again.
To eliminate the square root, we square both sides of the equation:
(5x - 1)^2 = (2√((x + 4)(x - 1)))^2.
Expanding the squares gives us:
25x^2 - 10x + 1 = 4((x + 4)(x - 1)).
Simplifying further, we obtain:
25x^2 - 10x + 1 = 4(x^2 + 3x - 4).
Step 11: Expand and simplify.
Expanding the right side of the equation gives us:
25x^2 - 10x + 1 = 4x^2 + 12x - 16.
Step 12: Collect like terms.
Combine like terms on both sides of the equation:
21x^2 - 22x + 17 = 0.
Step 13: Solve the quadratic equation.
You can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
Unfortunately, this equation does not factor easily. To find the solution, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
For the equation 21x^2 - 22x + 17 = 0, we have:
a = 21, b = -22, c = 17.
Solving for x using the quadratic formula, we get two possible solutions.
x = (-(-22) ± √((-22)^2 - 4 * 21 * 17)) / (2 * 21).
Simplifying further, we have:
x = (22 ± √(484 - 1428)) / 42
x = (22 ± √(-944)) / 42.
The square root of a negative number is not a real number, so this equation has no real solutions.
Therefore, the equation √(x + 4) - 2√(x - 1) = -1 has no real solutions.