Question

help me asap please

Answer 1

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

Answer 2

given:

${x}^{2} + 14x = - 49$

${x}^{2} + 14x + 49 = 0$

this quadratic is easily factored:

$(x + 7)(x + 7) = {(x + 7)}^{2}$

what value of X makes the quadratic equal zero?

$0 = {(x + 7)}^{2}$

let x = -7

${( - 7 + 7)}^{2} = 0$

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:

${(x + a)}^{2}$

where 'a' is a constant,

the solution is a double root.

Meaning both roots to the quadratic are equal.