(x+1)^2-6=y
Solve for x and y should be part of the final answer
(x+1)²=y+6
(x+1)=√(y+6)
x=√(y+6)-1
x = -1±√(y+6)
To solve the equation (x+1)^2-6=y, we will follow these steps:
Step 1: Expand the squared term.
(x+1)^2 becomes (x+1)(x+1), which simplifies to x^2+2x+1. Therefore, the equation becomes x^2+2x+1-6=y.
Step 2: Combine like terms.
Combine 1 and -6 to get -5. The equation becomes x^2+2x-5=y.
Step 3: Isolate the variable.
Rearrange the equation to isolate the variable, x. Move y to the other side of the equation by subtracting y from both sides: x^2+2x-5-y=0.
Step 4: Solve the quadratic equation.
The equation x^2+2x-5-y=0 is a quadratic equation. We can solve it using various methods like factoring, completing the square, or using the quadratic formula. For simplicity, we will use the quadratic formula:
x = (-b±√(b^2-4ac)) / (2a),
where a, b, and c correspond to the coefficients in the quadratic equation ax^2+bx+c=0.
In our case, the coefficients are:
a = 1
b = 2
c = -5-y
Substituting the values into the quadratic formula, we get:
x = (-2±√(2^2-4*1*(-5-y))) / (2*1).
This simplifies to:
x = (-2±√(4+20+4y)) / 2,
x = (-2±√(24+4y)) / 2,
x = -1±√(6+y).
Hence, the solutions for x are x = -1+√(6+y) and x = -1-√(6+y).
The corresponding value for y is the value you choose or is given.