Quadratic equation using factorization method

Examples

Solve the quadratic equation $x^2 + 7x + 10 = 0$ by factorization method.

Explanation:

Step 1: In the given equation, middle term is $+7$ and constant is $+10$. Find two numbers whose sum is $7$ and product is $10$. We get $2$ and $5$ as such numbers.

Step 2: Rewrite the quadratic equation as $x^2 + 2x + 5x + 10 = 0$.

Step 3: Group the first two terms and the last two terms as $(x^2 + 2x) + (5x + 10) = 0$

Step 4: Factor out the common terms from each group. We get $x(x + 2) + 5(x + 2) = 0$

Step 5: Factor out the common factor of $(x + 2)$. We get $(x + 2)(x + 5) = 0$

Step 6: Set each factor equal to zero and solve for $x$. We get $x = -2$ and $x = -5$

Therefore, the solutions of the given quadratic equation are $x = -2$ and $x = -5$

Solution:

$x^2 + 7x + 10 = 0$ $x^2 + 2x + 5x + 10 = 0$
$(x^2 + 2x) + (5x + 10) = 0$ $x(x + 2) + 5(x + 2) = 0$
$(x + 2)(x + 5) = 0$
$(x + 2)= 0$ and $(x + 5) = 0$
$x = -2$ and $x = -5$