3x (x+2)= 2 (x + 5) help solve this plz and also this equation 1/6 (x - 5 ) =1/2 (x + 6) ?
If possible plz explain how you got the answer because my teacher is really bad at teaching and don't want to ask her cuz she will be pissed that I didn't ask her earlier so plz help I don't want to fail math!!!!
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:-
1.
3x² + 6x = 2x + 10
3x² + 4x - 10 = 0
x = [ - 4 ± √( 16 + 120 ) ] / 6
x = [ - 4 ± √136 ] / 6
x = [ - 4 ± 2√34 ] / 6
x. = [ - 2 ± √34 ] / 3
2.
x - 5 = 3 ( x + 6 )
x = 3x + 23
- 23 = 2x
x. = - 23/2
Question 1:
Distribute:
3x²+6x=2x+10
Subtract 10 from both sides:
3x²+6x-10=2x+10-10
Simplify:
3x²+6x-10=2x
Subtract 2x from both sides:
3x²+6x-10-2x=2x-2x
Simplify:
3x²+4x-10=0
Use the quadratic formula:
x=[-2+√(34)]/3 or x=[-2-√(34)]/3
Answer: x=[-2+√(34)]/3 or x=[-2-√(34)]/3
Question 2:
Distribute:
1/6x-5/6=1/2x+3
Add 5/6 to both sides:
1/6x-5/6+5/6=1/2x+3+5/6
Simplify:
1/6x=1/2x+23/6
Subtract 1/2x from both sides:
1/6x-1/2x=1/2x+23/6-1/2x
Simplify:
-1/3x=23/6
Multiply both sides by -3:
x=-23/2
Answer: -23/2
Question 1) If you mean: 3x times (x+2) = 2 times (x+5)
Then: 3x^2 +6x = 2x+10)
Transposing and collecting like terms: 3x^2 +4x -10 = 0
Use the quadratic equation formula to solve for x:
x = -(2 + square root 34)/3 or x = (-2 + square root 34)/3
Question 2) If you mean: 1/6 times (x-5) = 1/2 times (x+6)
Then: x/6 -5/6 = 0.5x +3
Multiply all terms by 6: x -5 = 3x +18
Or: x -3x = 18+5 => -2x = 23
Divide both sides by -2: x = -11.5
3x (x+2)= 2(x + 5)
3x^2 + 6x – 2x – 10 = 0
3x^2 + 4x – 10 = 0
Use the quadratic formula
x = [-2 ± √(34)]/3
Or complete the square like this
3x^2 + 4x – 10 = 0
x^2 + (4/3)x = 10/3
Add (half the coefficient of x) squared, to both sides
x^2 + (4/3)x + 4/9 = 4/9 + 30/9
(x + 2/3)^2 = 34/9
x + 2/3 = ±√(34)]/3
x = [-2 ± √(34)]/3
(x - 5 )/6 = (x + 6)/2 multiply both sides by 6
x – 5 = 3x + 18
-23 = 2x
x = -23/2
3x.(x + 2) = 2.(x + 5)
3x² + 6x = 2x + 10
3x² + 4x = 10
x² + (4/3).x = 10/3
x² + (4/3).x + (2/3)² = (10/3) + (2/3)²
[x + (2/3)]² = 34/9
[x + (2/3)]² = [± (√34)/3]²
x + (2/3) = ± (√34)/3
x = - (2/3) ± [(√34)/3]
x = (- 2 ± √34)/3
x₁ = (- 2 ± √34)/3
x₂ = (- 2 ± √34)/3
(1/6).(x - 5) = (1/2).(x + 6)
(x - 5)/6 = (x + 6)/2
2.(x - 5) = 6.(x + 6)
2x - 10 = 6x + 36
2x - 6x = 36 + 10
- 4x = 46
x = - 46/4
x = - 23/2
3x (x+2)= 2 (x + 5)
Expand on the left and right, separately:
3x^2 + 6x = 2x + 10
Combine like terms and write in standard form:
3x^2 + 4x - 10 = 0
Use the quadratic formula:
x = (1/3) (-2 - √(34))
x = (1/3) (-2 + √(34))
1/6 (x - 5 ) =1/2 (x + 6)
Multiply both sides by 6:
x - 5 = 3 (x + 6)
Expand on the right:
x - 5 = 3x + 18
Combine like terms:
-2x = 23
Divide both sides by -2:
x = - 23/2