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Solve an equation example

Question:

Solve the equation: 12 x + square root of x - 1 = 0

Solution:

12 x + square root of x - 1 = 0
note: x = (square root of x)2
12 (square root of x)2 + (square root of x) - 1 = 0
let t = (square root of x)
12 t2 + t - 1 = 0

using formula, the roots of ax2 + bx + c = 0 is: x1,2 = [-b +- square root of (b2 - 4ac)]/2a. From the one variable second degree equation 12 t2 + t - 1 = 0, we get, a = 12, b = 1 c = -1

t1,2 = [-b +- square root of (b2 - 4ac)]/2a
= [-1 +- square root of (12 - 4 × 12 × (-1))]/2 × 12
= [-1 +- square root of (1 + 48)]/24
= [-1 +- square root of 49]/24
= [-1 +- 7]/24
t1 = (-1 + 7)/24 = 6/24 = 1/4
square root of x = 1/4
x = (1/4)2 = 1/16
t2 = (-1 - 7)/24 = -8/24 = -1/3
square root of x cannot be a negative number, so drop the negative solution.

Substitute x = 1/16 into the given equation, find the left side of the equation is equal to the right side of the equation, so x = 1/16 is the root of given equation.