Solve Quadratic Equations
If there is more than 1 variable, with different exponents, try to solve the problem by factoring.
The equation must be set equal to zero to use the zero product property.
When two or more factors multiply together and the result is zero, then one of the factors
must be zero.
Solve these quadratic equations by factoring and using the Zero Product Property.
t2 + 3t – 10 = 0
(t + 5)(t – 2) = 0
r2 – 12 = 4r
t+5=0 t–2=0
t+5=0 t–2=0
-5 -5 + 2 +2
t = -5 t = 2
9y2 – 1 = 0
10x2 – 5x = 0
If there is just 1 variable, get it alone.
Solve these quadratic equations by taking the square root.
You will need to take the square root of both sides of the equation.
9(x – 3)2 = 63
4(w + 3)2 – 81 = 0
Solve by completing the square.
x2 + 12x + 11 = 0
2x2 – 8x + 15 = 0
Solving Equations using the Quadratic Formula
The Quadratic Formula can be used to solve equations that contain an x2 term.
The equation must be set equal to zero, before you try to identify the coefficients.
ax2 + bx + c = 0
a is the coefficient to the squared variable.
b is the coefficient of the variable.
c is the constant number, not attached to a variable.
The only things you put into the formula are NUMBERS.
Remember to Simplify and Reduce your answers.
Quadratic Formula:
x2 + 3x – 5 = 0
a =1
b=3
c = -5
 3  ( 3) 2  4(1)( 5)
x
2(1)
x
3  9  20
2
x
3  29
2
 b  b 2  4ac
x
2a
3t2 – 2t + 1 = 0
Solve by using the quadratic formula.
4x2 – 4x – 11 = 0
9w2 + 30w = -23