Question #84aa9

2 Answers
Feb 1, 2018

x = (-13+-3sqrt(17))/2

Explanation:

x^2 = -13x - 4
Subtract -13x - 4 from both sides:
x^2 + 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) where a is the coefficient of x^2, b is the coefficient of x, c is the constant.

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

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

x = (-13+-sqrt(153))/2

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

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

x = (-13+-3sqrt(17))/2

Feb 1, 2018

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

Explanation:

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

Roots of a quadratic equation given by the formula,

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

Coefficient of term x^2 = a, coefficient of term x = 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