Question

2х^2 +11x+34=(x+6)^2

Answer 1

2x²+11x+34=(x+6)²
2x²+11x+34=x²+12x+36
2x²-x²+11x-12x+34-36=0
x²-x-2=0
D=1+8=9=3²
x₁=(1-3)/2=-2/2=-1
x₂=(1+3)/2=4/2=2

Answer 2

To solve the equation 2x^2 + 11x + 34 = (x + 6)^2, we need to expand the squared term on the right side of the equation and simplify the equation:

2x^2 + 11x + 34 = x^2 + 12x + 36

Next, let's bring all the terms to one side of the equation to set it equal to zero:

2x^2 + 11x + 34 - x^2 - 12x - 36 = 0

Simplifying further:

x^2 - x^2 + 2x^2 + 11x - 12x + 34 - 36 = 0

x^2 - x^2 cancels out, and combining like terms:

2x^2 - x^2 + 11x - 12x + 34 - 36 = 0

x^2 - x + -2 = 0

Now we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -1, and c = -2. To solve this quadratic equation, we can factor it or use the quadratic formula.

Let's solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values, we get:

x = (-(-1) ± √((-1)^2 - 4(1)(-2))) / (2(1))

Simplifying further:

x = (1 ± √(1 + 8)) / 2

x = (1 ± √9) / 2

x = (1 ± 3) / 2

Now we have two solutions:

x1 = (1 + 3) / 2 = 4 / 2 = 2

x2 = (1 - 3) / 2 = -2 / 2 = -1

Therefore, the solutions to the equation 2x^2 + 11x + 34 = (x + 6)^2 are x = 2 and x = -1.