To solve this equation, we need to combine like terms on both sides and then simplify:
2x^2 - 2x + 34 = -6x^2 - 34x + 10
First, let's bring all the terms to one side of the equation:
2x^2 - 2x + 34 + 6x^2 + 34x - 10 = 0
Combine the x^2 terms:
8x^2 - 2x + 34x - 10 = 0
Combine the x terms:
8x^2 + 32x - 10 = 0
Now, let's factor out the common factor:
2(4x^2 + 16x - 5) = 0
Now, we need to solve for x by setting each factor equal to zero:
4x^2 + 16x - 5 = 0
Using the quadratic formula, we find:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-16 ± √(16^2 - 44(-5))) / 2*4
x = (-16 ± √(256 + 80)) / 8
x = (-16 ± √336) / 8
x = (-16 ± 18.33) / 8
x = 2.33 or x = -3.33
So, the solutions to the equation are x = 2.33 or x = -3.33.
To solve this equation, we need to combine like terms on both sides and then simplify:
2x^2 - 2x + 34 = -6x^2 - 34x + 10
First, let's bring all the terms to one side of the equation:
2x^2 - 2x + 34 + 6x^2 + 34x - 10 = 0
Combine the x^2 terms:
8x^2 - 2x + 34x - 10 = 0
Combine the x terms:
8x^2 + 32x - 10 = 0
Now, let's factor out the common factor:
2(4x^2 + 16x - 5) = 0
Now, we need to solve for x by setting each factor equal to zero:
4x^2 + 16x - 5 = 0
Using the quadratic formula, we find:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-16 ± √(16^2 - 44(-5))) / 2*4
x = (-16 ± √(256 + 80)) / 8
x = (-16 ± √336) / 8
x = (-16 ± 18.33) / 8
x = 2.33 or x = -3.33
So, the solutions to the equation are x = 2.33 or x = -3.33.