What are the solutions to the equation ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 ?

The solutions to the equation ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 are x=-2,x= 8/7

Find the zeros of ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8

The zeros of ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 are x=-2,x= 8/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{( 3 x - 1 ) ^{2}}{16} - (x - \frac{1}{4}) (x + \frac{1}{4}) = - \frac{7}{8}

x = - 2, x = \frac{8}{7}

Decimal Notation

x = - 2, x = 1.14285 \dots

Solution steps

\frac{( 3 x - 1 ) ^{2}}{16} - (x - \frac{1}{4}) (x + \frac{1}{4}) = - \frac{7}{8}

Find Least Common Multiplier of

16, 8 : 16

Multiply by LCM=

16

\frac{( 3 x - 1 ) ^{2}}{16} \cdot 16 - (x - \frac{1}{4}) (x + \frac{1}{4}) \cdot 16 = - \frac{7}{8} \cdot 16

Simplify

(3 x - 1)^{2} - 16 (x - \frac{1}{4}) (x + \frac{1}{4}) = - 14

Expand

(3 x - 1)^{2} - 16 (x - \frac{1}{4}) (x + \frac{1}{4}) : - 7 x^{2} - 6 x + 2

- 7 x^{2} - 6 x + 2 = - 14

Move

14

to the left side

- 7 x^{2} - 6 x + 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 ( - 7 ) \cdot 16}{2 ( - 7 )}

(- 6)^{2} - 4 (- 7) \cdot 16 = 22

x_{1, 2} = \frac{- ( - 6 ) \pm 22}{2 ( - 7 )}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 22}{2 ( - 7 )}, x_{2} = \frac{- ( - 6 ) - 22}{2 ( - 7 )}

x = \frac{- ( - 6 ) + 22}{2 ( - 7 )} : - 2

x = \frac{- ( - 6 ) - 22}{2 ( - 7 )} : \frac{8}{7}

The solutions to the quadratic equation are:

x = - 2, x = \frac{8}{7}

x^{2} + 6 x + 10 = - x

x, 4 x^{2} + 2 x y + 4 y^{2} = 1

A, (A - 1)^{2} + (B - 2)^{2} = 0

10 m^{2} - 19 = 0

2 x^{2} - (x + 1)^{2} + 3 x = 2 x (x - 2) + 5

What are the solutions to the equation ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 ?
The solutions to the equation ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 are x=-2,x= 8/7
Find the zeros of ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8
The zeros of ((3x-1)^2)/(16)-(x-1/4)(x+1/4)=-7/8 are x=-2,x= 8/7