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Solve x2 14x = −24 by completing the square. what is the solution set of the equation?
a. {−12, −2}
b. {−7, 7}
c. {−6, −4}
d. {−5, 5}

Respuesta :

MissPhiladelphia
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 roots of the quadratic equation can be find out using the split the middle term method. The solution set of the equation is (-12,-2). Thus the option a is the correct option.

The solution of the set of the equation has to find out. The given equation is the quadratic equation.

What is quadratic equation?

A quadratic equation is the equation in which the highest power of the variable is two. The roots of the quadratic equation can be find out using the split the middle term method.

Given information-

The equation given in the problem is,

[tex]x^2+14x=-24[/tex]

Rearrange the equation as,

[tex]x^2+14x+24=0[/tex]

Split the middle term,

[tex]x^2+12x+2x+24=0[/tex]

Make groups,

[tex]x(x+12)+2(x+12)=0\\(x+12)(x+2)=0\\[/tex]

The above factorization is the required factorization.

The first roots of the equation is,

[tex]x+12=0\\x=-12[/tex]

The another root of the equation is,

[tex]x+2=0\\x=-2[/tex]

Hence the solution set of the equation is (-12,-2). Thus the option a is the correct option.

Learn more about the quadratic equation;

https://brainly.com/question/17177510