QuestionSolve for : . Find all solutions for .
Studdy Solution
STEP 1
Assumptions1. The equation to solve is . . The variable to solve for is .
STEP 2
First, we need to expand the right side of the equation, which is a square of a binomial. The square of a binomial is given by .
STEP 3
Substitute the expanded form of back into the equation.
STEP 4
To solve for , we need to bring all terms to one side of the equation to set it equal to zero. Subtract , , and from both sides of the equation.
STEP 5
implify the equation by combining like terms.
STEP 6
Now, we need to factor the quadratic equation. A quadratic equation can be factored into , where and are the roots of the equation.
STEP 7
To find the values of and , we need to find two numbers that multiply to (the constant term) and add to (the coefficient of ). The numbers and satisfy these conditions.
STEP 8
Setting each factor equal to zero gives the solutions to the equation.
STEP 9
olving each equation gives the solutions for .
The solutions for are and .
Was this helpful?