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Solving Quadratic Equations
Examples: Non-examples:
Solving Quadratic Equations A quadratic equation in one variable is an equation that can be written in the form ax2 + bx + c = 0, where x is the variable.
23x + 8x +4 = 0
2x = 182
(x + 2)(x - 6) = 0
x4 = 100
22 = 18x
33x +8x + 4 = 0
(x + 2) + (x - 6) = 0
24x = 100
Example 1 Solve the equation.
Solving Quadratic Equations x2 = k means or
2x = 64
x = k x = - k
Example 2 Solve the equation.
Solving Quadratic Equations x2 = k means or
2x -144 = 0
x = k x = - k
Example 3 Solve the equation.
Solving Quadratic Equations x2 = k means or
2(x - 2) = 144
x = k x = - k
Example 4 Solve the equation.
Solving Quadratic Equations x2 = k means or
2(3x + 4) = 25
x = k x = - k
Example 5 Solve the equation.
Solving Quadratic Equations x2 = k means or
26(8 - x) = 0
x = k x = - k
Example 6 Solve the equation.
Solving Quadratic Equations x2 = k means or
21 x - 8 = 08
x = k x = - k
Solving Quadratic Equations by Factoring
Example 1 Solve the equation.
Solving Quadratic Equations by Factoring
(x + 2)(x - 6) = 0
If a·b = 0, then a = 0 or b = 0.
Example 2 Solve the equation.
Solving Quadratic Equations by Factoring
2x - 9x -10 = 0
If a·b = 0, then a = 0 or b = 0.
Example 3 Solve the equation.
Solving Quadratic Equations by Factoring
2x -10x + 25 = 0
If a·b = 0, then a = 0 or b = 0.
Example 4 Solve the equation.
Solving Quadratic Equations by Factoring
23x + 8x + 4 = 0
If a·b = 0, then a = 0 or b = 0.
Solving Equations by Factoring (Advanced)
Example 1 Solve the equation.
Solving Equations by Factoring (Advanced)
212x - 40x + 12 = 0
If a·b = 0, then a = 0 or b = 0.
Example 2 Solve the equation.
Solving Equations by Factoring (Advanced)
210 -10x = 0
If a·b = 0, then a = 0 or b = 0.
Example 3 Solve the equation.
Solving Equations by Factoring (Advanced)
3x - 25x = 0
If a·b = 0, then a = 0 or b = 0.
Example 4 Solve the equation.
Solving Equations by Factoring (Advanced)
327x = 3x
If a·b = 0, then a = 0 or b = 0.
