Respuesta :

Alexisld
x2 + 14X = -49
+49
x2 + 14X + 49
(x2 + 14X + 7) + 49 - 7 = 0
(X+7)2 + 42 = 0
- 42
(x+7)2 = 42
*square root of both sides)
X + 7 = square root of 42
-7
X = -7 +/- square root of 42

x = -13.48
x = -0.52

and for b, without doing any work my guess is because there is a 0 under the radical, which gives you only one real solution
sdgismep6d4p4
given:

[tex] {x}^{2} + 14x = - 49[/tex]

[tex] {x}^{2} + 14x + 49 = 0[/tex]

this quadratic is easily factored:

[tex](x + 7)(x + 7) = {(x + 7)}^{2} [/tex]

what value of X makes the quadratic equal zero?

[tex]0 = {(x + 7)}^{2} [/tex]

let x = -7

[tex] {( - 7 + 7)}^{2} = 0[/tex]

this is the only value that makes the equation equal to zero.

thus, there is a double root, which is equal to -7

for part 2:

Since it is quadratic, it will always have two roots. This means both roots are equal to -7

generally, whenever a quadratic factors into a perfect square of sums, like:

[tex] {(x + a)}^{2} [/tex]

where 'a' is a constant,

the solution is a double root.

Meaning both roots to the quadratic are equal.

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