Question

Square root the quadratic equation: x^2 + 14x + 48 = 0

(Please list the steps used, thank you).

Answer 1

Step-by-step explanation:4.2 Solving x2+14x+48 = 0 by Completing The Square . Subtract 48 from both side of the equation : x2+14x = -48Now the clever bit: Take the coefficient of x , which is 14 , divide by two, giving 7 , and finally square it giving 49 Add 49 to both sides of the equation : On the right hand side we have : -48 + 49 or, (-48/1)+(49/1) The common denominator of the two fractions is 1 Adding (-48/1)+(49/1) gives 1/1 So adding to both sides we finally get : x2+14x+49 = 1Adding 49 has completed the left hand side into a perfect square : x2+14x+49 = (x+7) • (x+7) = (x+7)2 Things which are equal to the same thing are also equal to one another. Since x2+14x+49 = 1 and x2+14x+49 = (x+7)2 then, according to the law of transitivity, (x+7)2 = 1We'll refer to this Equation as Eq. #4.2.1 The Square Root Principle says that When two things are equal, their square roots are equal.Note that the square root of (x+7)2 is (x+7)2/2 = (x+7)1 = x+7Now, applying the Square Root Principle to Eq. #4.2.1 we get: x+7 = √ 1 Subtract 7 from both sides to obtain: x = -7 + √ 1 Since a square root has two values, one positive and the other negative x2 + 14x + 48 = 0 has two solutions: x = -7 + √ 1 or x = -7 - √ 1

Answer 2

x = - 8 , x = - 6

Explanation:

Assuming you require the roots of the quadratic equation.

x² + 14x + 48 = 0

consider the factors of the constant term (+ 48) which sum to give the coefficient of the x- term (+ 14)

the factors are 8 and 6 , since

8 × 6 = 48 and 8 + 6 = 14

use these factors to split the x- term

x² + 8x + 6x + 48 = 0 ( factor the first/second and third/fourth terms )

x(x + 8) + 6(x + 8) = 0 ← factor out (x + 8) from each term

(x + 8)(x + 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ( subtract 8 from each side )

x = - 8

x + 6 = 0 ( subtract 6 from both sides )

x = - 6

The roots of the equation are x = - 8 and x = - 6