factor and solve
6d^2 + 2d = 10d + 35
The first step in factoring is to move everything to one side.
6d^2 + 2d = 10d + 35
6d^2 - 8d - 35 = 0.
However, I cannot find real roots for this equation. Are you sure you typed it correctly?
I checked it and that is how it is on the worksheet I couldn't get it to work out either
You can find irrational factors using the quadratic equation.
For ax^2 + bx + c, x = (-b +/- sqrt(b^2 -4ac))/(2a).
6d^2 - 8d - 35 = 0
d = (8 +/- sqrt(64 - 4(6)(-35)))/(2*6)
To factor and solve the given equation: 6d^2 + 2d = 10d + 35
Step 1: Start by bringing all terms to one side to set the equation equal to zero:
6d^2 + 2d - 10d - 35 = 0
Step 2: Combine like terms:
6d^2 - 8d - 35 = 0
Step 3: Now, we need to factor the quadratic equation. Since the coefficient of the term with d^2 is not 1, we use the quadratic formula to find the roots or solve the equation. The quadratic formula is:
d = (-b ± √(b^2 - 4ac)) / (2a)
Applying the formula to our equation, where a = 6, b = -8, and c = -35:
d = (-(-8) ± √((-8)^2 - 4(6)(-35))) / (2(6))
d = (8 ± √(64 + 840)) / 12
d = (8 ± √904) / 12
d = (8 ± 2√226) / 12
d = (2 ± √226) / 3
So the solutions to the quadratic equation 6d^2 + 2d = 10d + 35 are:
d = (2 + √226) / 3 and d = (2 - √226) / 3