Question

6x(2x+3)+2(4-3x)=26. Решит задачу

Answer 1

6x(2x+3)+2(4-3x)=26
6x(2x+3)+2(4-3x)-26=0
2(3x(2x+3)+4-3x-13)=0
2(6x²+6x-9)=0
2*3(2x²+2x-3)=0
2x²+2x-3=0
x=-2+-√(2²-4*2*(-3)) /2*2
x=-2+-√(4+24) / 4
x=-2+-√28 /4
x=-2+2√2 /4
x=-2-2√2 /4
x=-1+√7 /2
x=-1-√7 /2

Answer 2

To solve the equation 6x(2x+3) + 2(4-3x) = 26, follow these steps:

Step 1: Expand and simplify the equation Expand the terms on the left-hand side of the equation:

6x(2x+3) + 2(4-3x) = 26

12x^2 + 18x + 8 - 6x = 26

Step 2: Bring all terms to one side to set the equation to zero Subtract 26 from both sides:

12x^2 + 18x + 8 - 6x - 26 = 0

Step 3: Combine like terms:

12x^2 + 12x - 18 = 0

Step 4: Divide by the common factor (in this case, 6):

2x^2 + 2x - 3 = 0

Step 5: Solve the quadratic equation

To solve this quadratic equation, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 2, and c = -3.

x = ( -2 ± √(2² - 4 * 2 * -3) ) / 2 * 2

x = ( -2 ± √(4 + 24) ) / 4

x = ( -2 ± √28 ) / 4

Now, calculate the two possible solutions:

x₁ = ( -2 + √28 ) / 4 x₂ = ( -2 - √28 ) / 4

Step 6: Simplify the solutions

x₁ = ( -2 + √28 ) / 4 ≈ 0.56155 x₂ = ( -2 - √28 ) / 4 ≈ -1.06155

So, the two solutions for the equation are approximately x ≈ 0.56155 and x ≈ -1.06155.