Lesson Example Discussion Quiz: Class Homework |
Step-206 |
Title: Quadratic-Equations and Factors |
Grade: 10-a Lesson: S2-L1 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Solve the quadratic equation: \$4x^2 + 8x + 14 = 0\$. |
|
2 |
Step |
Simplify the equation |
\$2(2x^2 + 4x + 7) = 0\$ \$2x^2 + 4x + 7 = 0\$ |
3 |
Formula: |
To solve the quadratic equation \$2x^2 + 4x + 7 = 0\$, we can use the quadratic formula. The quadratic formula states that for an equation in the form \$ax^2 + bx + c = 0\$, the solutions for x can be found using the formula |
\$x = (-b ± \sqrt (b^2 - 4ac)) / (2a)\$ |
4 |
Hint |
For the equation \$2x^2 + 4x + 7 = 0\$ then, substituting these values into the quadratic formula, we get |
a = 2, b = 4, and c = 7 \$x = (- 4 ± \sqrt (4^2 - 4 times 2 times 7)) / (2 times 2)\$ \$x = (- 4 ± \sqrt (- 40)) / 4\$ |
5 |
Step |
After simplification |
\$x = (- 4 ± \sqrt (2^2 i^2 5)) / 4\$ \$x = (- 4 ± 2i \sqrt 5) / 4\$ \$x = (- 2 ± i \sqrt 5) / 2\$ |
6 |
Step |
This gives us two possible solutions |
\$x_1 = (- 2 + i \sqrt 5) / 2\$ and \$x_2 = (- 2 - i \sqrt 5) / 2 \$ |
7 |
Answer |
Option |
A |
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