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Example Questions
Example Question #11 : Solving By Other Methods
Solve the following by using the Quadratic Formula:
No solution
The Quadratic Formula:
Plugging into the Quadratic Formula, we get
*The square root of a negative number will involve the use of complex numbers
Therefore,
Example Question #11 : Solving By Other Methods
A rectangular yard has a width of w and a length two more than three times the width. The area of the yard is 120 square feet. Find the length of the yard.
24 feet
20 feet
6 feet
89 feet
5 feet
20 feet
The area of the garden is 120 square feet. The width is given by w, and the length is 2 more than 3 times the width. Going by the order of operations implied, we have length given by 3w+2.
(length) x (width) = area (for a rectangle)
In order to solve for w, we need to set the equation equal to 0.
To solve this we should use the Quadratic Formula:
(reject)
The width is 6 feet, so the length is or 20 feet.
Example Question #11 : Solving By Other Methods
Complete the square to solve for in the equation
or
1) Get all of the variables on one side and the constants on the other.
2) Get a perfect square trinomial on the left side. One-half the x-term, which will be squared. Add squared term to both sides.
3) We have a perfect square trinomial on the left side
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Example Question #11 : Solving By Other Methods
Solve the following quadratic equation for x by completing the square:
or
or
or
or
This quadratic equation needs to be solved by completing the square.
1) Get all of the x-terms on the left side, and the constants on the right side.
2) To put this equation into terms are more common with completing the square, we can make a coefficient of 1 in front of the term.
3) We need to make the left side of the equation into a "perfect square trinomial." To do this, we take one-half of the coefficient in front of the x, square it, and add it to both sides.
The left side is a perfect square trinomial.
4) We can represent a perfect square trinomial as a binomial squared.
5) Take the square root of both sides
6) Solve for x
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