Solve the equation 6 2x 4 2 2x 4 2

Asked by maham237 @ 19/07/2021 in Mathematics viewed by 298 People

Answered by maham237 @ 19/07/2021

ANSWER
$x = - \frac{5}{3}$

or

$x = - \frac{9}{4}$

EXPLANATION

We want to solve the equation,

$6 {(2x + 4)}^{2} = (2x + 4) + 2$

One interesting way to solve this equation is to equate everything to zero and solve as quadratic equation by factoring.

$6 {(2x + 4)}^{2} - (2x + 4) - 2 = 0$

The above is a quadratic equation in
$(2x + 4)$

where

$a=6,b=1,c=-2$

and
$a \times c = - 2 \times 6 = - 12$

We use the factors,
$-4,3$
to split the middle term to get,

$6 {(2x + 4)}^{2} + 3 (2x + 4) - 4(2x + 4) - 2 = 0$

We factor to obtain,

$3 (2x + 4)[2(2x + 4) + 1] - 2 [ 2 (2x + 4) + 1]= 0$

We factor further to obtain,

$(3(2x + 4) - 2)(2(2x + 4) + 1) = 0$

$(6x + 12 - 2)(4x + 8 + 1) = 0$

$(6x + 10)(4x + 9) = 0$

$x = - \frac{10}{6} = - \frac{5}{3}$

or

$x = - \frac{9}{4}$

Solve the equation 6 2x 4 2 2x 4 2

Similar Questions

A student is solving the equation 2x 1 16x 2

5x 4 6 4x 1 3x 10 2 solve

Solve 2x 2 x 4 0 by completing the square

Solve the equation graphically 2x y 2 4x y 4

Solve for x 1 x 2 2x 1 6 x

X 4 x 3 2x 2 x 1 x 1

2 4 solving equations with the variable on each side

X 3y 6 2x 3y 12 solve by substitution method

Solve 2x 2 7x 3 0

Solve 2x 2 7x 15 0 by completing the square

Which equation is true for x 6 and x 2

Solve the equation 4 x 3 5 2x 3

Solve 4 x 3 2 x 1 0

4 2x 1 2 x 5 5 x 1 3

7 6 4 6 2 6 1 6 _ 6

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220