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Question

27x+4=40x^2

Answer 1

27x + 4 = 40x²

Transpose 27x

27x + 4 - 27x = 40x² - 27x

4 = 40x² - 27x

Transpose 4

4 - 4 + 40x² - 27x - 4

0 = 40x² - 27x - 4

The middle term is - 27x

Find the sum of the middle term

Multiply the first term 40 times the last term 4 equals 160 and factor

Factor of 160

1 x 160
2 x 80
4 x 40
5 x 32. . .←. .use these factors
8 x 20
10 x 16

+ 5 and - 32 satisfy the sum of the middle term

Insert + 5x and - 32x into the equation

0 = 40x² - 27x - 4

0 = 40x² + 5x - 32x - 4

0 = 5x(8x + 1) - 4(8x + 1)

0 = (5x + 4)(8x + 1)

- - - - - - - - -s-

Answer 2

This is a quadratic equation.

Factor it like a polynominal
-40x^2+27x+4
(8x+1) (5x+4)
When you write it as a fraction, make the x number the bottom number of the fraction.
x=1/8 or x=4/5

Answer 3

27x+4=40x^2

40x^2 - 27x - 4 = 0

In situations like this where it is not obvious what the factors are (or if there even are integer factors), use the quadratic formula.

x = [27 +/- sqrt(27^2 - 4*40*-4)] / 2*40
x = [27 +/- sqrt(729 + 640)] / 80
x = [27 +/- sqrt(1369)] / 80
x = [27 +/- 37] / 80
x = 64/80, -10/80
x = 4/5, -1/8

Answer 4

27x+4=40x^2

40x² - 27x - 4 = 0

factor

(8x + 1)(5x - 4) = 0

x = -1/8, x = 4/5
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