Mathematics Quarter 1

MATHEMATICS QUARTER 1
SOLVING QUADRATIC EQUATIONS BY EXTRACTING
SQUARE ROOTS
Example 1: USING SQUARE ROOTS TO SOLVE x2 = c
Solve by extracting the square roots. A. x2 = 64
Solution: x2 = 64 √x2 = √64 x = ±8
The solutions are 8 and -8
Example 2: USING SQUARE ROOTS TO SOLVE QUADRATIC EQUATIONS
Solution: Solve by extracting the square roots.
A. x2 + 6 = 6
Solution: x2 + 6 = 6×2 + 6 − 6 = 6 − 6 Subtract 6 from both sides x2 = 0 √x 2 = ±√0
Take the square root of both sides: x = 0
The solution is 0.
Solving quadratic equations by extracting roots is applicable if the equation is in the form
ax2 + c = 0 where A and C are real numbers and a ≠ 0. Below are the steps in
Solving this type of quadratic equation.
1. Write the equation in the form: x2 =c/a
2. Extract the square roots of both side of the equation. Put a ± sign before the square
root of the number. Use the ± roots to solve for the resulting equation.
3. Check your answer by substitution to see whether the equation is true.
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