1. Solving Quadratic Equations using Square Roots
9.3
Solving Quadratic Equations using Square Roots
Students will be able solve quadratic equations using square roots.
Students will be able to approximate the solutions (values) of quadratic equations.

2. Students will be able solve quadratic equations using square roots.
We just studied properties of square roots.
Now we will use square roots to solve quadratic equations of the form 𝑎 𝑥 2 +𝑐=0.
We will first isolate 𝑥 2 on one side of the equation to obtain 𝑥 2 =𝑑.
Then solve by taking the square root of each side.

3. Students will be able solve quadratic equations using square roots.
Possible solutions to 𝑥 2 =𝑑
When 𝑑>0, 𝑥 2 =𝑑 has two real solutions, 𝑥=± 𝑑 .
When 𝑑=0, 𝑥 2 =𝑑 has one real solutions, 𝑥=0.
When 𝑑<0, 𝑥 2 =𝑑 has no real solutions.
Like 𝑥 2 =9, therefore, 𝑥=±3
Because 0 =0 and that is all.
Because we cannot take the square root of a negative number and get a real solution. So there is no real solution

4. Students will be able solve quadratic equations using square roots.
Solve 3 𝑥 2 −27=0 using square roots.
Add 27 to each side.
Divide each side by 3.
Take the square root of each side.
Simplify.
The solutions are 𝑥=3 and 𝑥=−3.

5. Students will be able solve quadratic equations using square roots.
Solve 𝑥 2 −10=−10 using square roots.
The only solution is 𝑥=0.

6. Students will be able solve quadratic equations using square roots.
Solve −5𝑥 2 +11=16 using square roots.
The square of a real number cannot be negative.
So, the equation has no real solution.

7. Students will be able solve quadratic equations using square roots.
Solve (𝑥−1) 2 =25 using square roots.
Since we already have the squared part alone
Take the square root of both sides.
Simplify
Add 1 to both sides.
So, the solutions are 𝑥=1+5=6 and 𝑥=1−5=−4.
That is, 𝑥=6 and 𝑥=−4.
Simplify.

8. Students will be able solve quadratic equations using square roots.
You Trys!!
No real solution.
Two real solutions.
No solution.
One real solution.

9. Students will be able solve quadratic equations using square roots.
You Trys!!
and
and

10. 2. Students will be able to approximate the solutions (values) of quadratic equations.
Solve 4𝑥 2 −13=15 using square roots. Round the solution to the nearest hundredth.
Add 13 to each side.
Divide each side by 4.
Take the square root of each side.
Use a calculator.
The solutions are 𝑥≈2.65 and 𝑥≈−2.65

11. 2. Students will be able to approximate the solutions (values) of quadratic equations.
You Tries! Solve the equation using square roots. Round the solution to the nearest hundredth.
Add 2 to each side.
Divide each side by 5.
Take the square root of each side.
Use a calculator.
The solutions are 𝑥≈0.63 and 𝑥≈−0.63