Question

Solve for x in the equation x2+2x+ 1 = 17.

Ox=-1+ 15
Ox=-1+17
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Answer 1

For this case we must solve the following quadratic equation:

`x ^ 2 + 2x + 1 = 17`

Subtracting 17 from both sides of the equation we have:

`x ^ 2 + 2x + 1-17 = 0\\x ^ 2 + 2x-16 = 0`

The solution of the equation is given by:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}`

Where:

`a = 1\\b = 2\\c = -16`

Substituting the values we have:

`x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 16)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 64}} {2}\\x = \frac {-2 \pm \sqrt {68}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 17}} {2}\\x = \frac {-2 \pm2 \sqrt {17}} {2}\\x = -1 \pm \sqrt {17}`

Thus, we have two roots:

`x_ {1} = - 1+ \sqrt {17}\\x_ {2} = - 1- \sqrt {17}`

Answer:

`x_ {1} = - 1+ \sqrt {17}\\x_ {2} = - 1- \sqrt {17}`