Question

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

Answer 1

x = negative 1 plus-or-minus StartRoot 17 EndRoot

Answer 2

`x = - 1 + √(17)\\and\\x = - 1 - √(17)\\`

Explanation:

given equation

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

subtracting 17 from both sides

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

the solution for quadratic equation

`ax^2 + bx + c = 0` is given by

x =
`x = -b + √(b^2 - 4ac) /2a \\\\and \ \\-b - √(b^2 - 4ac) /2a`

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in our problem

a = 1

b = 2

c = -16

`x =( -2 + √(2^2 - 4*1*-16)) /2*1 \\x =( -2 + √(4 + 64)) /2\\x =( -2 + √(68) )/2\\x = ( -2 + √(4*17) )/2\\x = ( -2 + 2√(17) )/2\\x = - 1 + √(17)\\and\\\\x = - 1 - √(17)\\`

thus value of x is

`x = - 1 + √(17)\\and\\x = - 1 - √(17)\\`