Question

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3x( 4x +7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11

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Answer 1

Answer:

x = 1 3/11

Step-by-step explanation:

3x( 4x + 7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11

Step 1: Left side do each math in parentheses.

( 12x + 21x ) + ( 24 + 6 ) = 11( 2x + 3 ) + 11

Step 2: Combine like terms on the left side.

33x + 30 = 11( 2x + 3 ) + 11

Step 3: Right side do each math in parentheses.

33x + 30 = 22x + 33 + 11

Step 4: Combine like terms on the right side.

33x + 30 = 22x + 44

Step 5: Subtract lowest non-variable from the highest non-variable

33x = 22x + 14

Step 6: Subtract variable on opposite side you just subtracted non-variable

11x = 14

Step 7: Divide 14 by number multiplied with the variable or just (14/11)

x= 1 3/11

Answer 2

Answer:

$x=\dfrac{1 +\sqrt{673}}{24}, \quad x=\dfrac{1 -\sqrt{673}}{24}$

Step-by-step explanation:

Given equation:

$3x( 4x +7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11$

Distribute the parentheses:

$\implies 12x^2+21x+24+6=22x+33+11$

$\implies 12x^2+21x+30=22x+44$

Subtract 22x from both sides:

$\implies 12x^2+21x+30-22x=22x+44-22x$

$\implies 12x^2-x+30=44$

Subtract 44 from both sides:

$\implies 12x^2-x+30-44=44-44$

$\implies 12x^2-x-14=0$

Use the quadratic formula to solve for x.

Quadratic Formula

$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0$

$\implies a=12, \quad b=-1, \quad c=-14$

Therefore:

$\implies x=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(12)(-14)}}{2(12)}$

$\implies x=\dfrac{1 \pm \sqrt{1+673}}{24}$

$\implies x=\dfrac{1 \pm \sqrt{673}}{24}$