Question #84aa9

2 Answers
Feb 1, 2018

x = (-13+-3sqrt(17))/2x=13±3172

Explanation:

x^2 = -13x - 4x2=13x4
Subtract -13x - 413x4 from both sides:
x^2 + 13x + 4 = 0x2+13x+4=0

Since it doesn't neatly factor, one of the simplest ways to calculate it is the quadratic formula:

x = (-b+-sqrt(b^2-4ac))/(2a)x=b±b24ac2a where aa is the coefficient of x^2x2, bb is the coefficient of xx, cc is the constant.

Substitute the values for a (1)a(1), b (13)b(13), and c (4)c(4)...

x = (-(13)+-sqrt((13)^2-4(1)(4)))/(2(1))x=(13)±(13)24(1)(4)2(1)

x = (-13+-sqrt(153))/2x=13±1532

sqrt(153)153 can also be represented as 3*sqrt(17)317 (because

sqrt(153) = sqrt(9 * 17) = sqrt(3^2 * 17)153=917=3217), so it could also be shown as

x = (-13+-3sqrt(17))/2x=13±3172

Feb 1, 2018

x = color(blue)(-0.3153), color(red)(-12.6847x=0.3153,12.6847

Explanation:

Given : x^2 + 13x +4 = 0x2+13x+4=0

Roots of a quadratic equation given by the formula,

x = (-b +- sqrt(b^2 - 4ac)) / (2a)x=b±b24ac2a where

Coefficient of term x^2 = ax2=a, coefficient of term x = bx=b and coefficient of constant term = c

:. x = (-13 +- sqrt(13^2 - (4 * 1 * 4))) / (2 * 1)

x = (-13 +- sqrt153)/2 = color(blue)(-0.3153), color(red)(-12.6847