In your own words, explain how to solve a quadratic equation by completing the square. Demonstrate the process with your own example.
To solve an equation using completing the square, you take half the “b” term and square it. That’s what you need to add and subtract (so the equation doesn’t change value). Once you have completed the square, you take the root of both sides. Then you can easily solve for x.
x^2-3x-4 = 0
Take the half the b term and square it.
(-3/2)^2 = 9/4
Add and subtract that:
(x^2-3x+9/4)-4-9/4 = 0
Simplify:
(x-3/2)^2 = 25/4
Square root:
x-3/2 = +/- 5/2
Add 3/2:
x = 3/2 +/- 5/2
x = -1 or 4
In your own words, explain how to solve a quadratic equation using the quadratic formula. Demonstrate the process with your own example.
To solve an equation, you plug the values of a, b, and c into the formula and then simplify. The formula is x = (-b +/- sqrt(b^2-4ac))/(2a)
x^2-3x-4 = 0
x = (3 +/- sqrt(3^2-4*1*-4))/2
x = (3 +/- sqrt(25)/2
x = (3 +/- 5)/2
x = -1 or 4
Mathlab checkpoint. Make sure the questions haven’t changed.
Number 1:
Sol: √7, -√7
Inter: (√7, 0), (-√7, 0)
Number 2:
4, 10
Number 3:
-3, 17
Number 4:
10 + √110, 10 - √110
Number 5:
-7, 3
Number 6:
Sol:
Inter:
Number 7:
0.7
Number 8:
-9 + √77, -9 - √77
Number 9:
Number 10:
Sol:
Inter:
Number 11:
6, 7
Number 12:
-10, 24
Number 13:
Exact =
Approx = 0.541, -5.541
Number 14:
6
Number 15:
No solution
Number 16:
9, 12
Number 17:
First = 22.21
Second = 17.21
Number 18, 19, 20, 21 done
Number 22:
x^2 + 13x + 22
Number 23:
x^2 – 18x + 81
Number 24:
x^2 – 12x + 36
Number 25:
Number 26: