First, rearrange the equation so that only zero will be on the right side:
x^2 + 14x +24 = 0
Let the coefficients be:
a = 1
b = 14
c = 24
To complete the square, add (b/2)^2 to both sides of the equation:
(b/2)^2 = 49
x^2 + 14x + 49 + 24 = 49
x^2 + 14x + 49 = 25
(x+7)^2 = 25
Therefore, the solution set of the equation is {-12, -2}
The solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
x² + 14x = −24
It is required to solve the equation by completing the square.
First, arrange the quadratic equation
x² + 14x + 24 = 0
x² + 14x + 7² - 7² + 24 = 0
(x + 7)² -25 = 0
(x + 7)² = 25
x + 7 = ±5
Taking positive sign:
x + 7 = 5
x = -2
Taking negative sign:
x + 7 = -5
x = -12
The solution set is [-12, -2]
Thus, the solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.
Learn more about quadratic equations here:
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