Solve 1= (y+3)(2y-2)
Use foil on the right side.
1 = 2y^2 +6y -2y -6 so 1 = 2y^2 +4y -6
Now subtract 1 from boths sides giving us
0 = 2y^2 +4y -7 Now we need two numbers that multiply to be 2*(-7) or -14 and add to be 4. There doesn't appear to be any number so we will use the quadratic formula.
x =[ -b +/- sqr(b^2 -4ac)]/(2a)
Now a = 2, b = 4 and c = -7
x = [-4 +/- sqr(16+56)]/4
x = [-4 +/- sqr72]/4
x = [-4 +/- sqr(36*2)]/4 Factored the radicand
now 36 is a perfect square so we have
x = [-4 +/- 6*sqr2] /4 Now take a 2 out of every term giving us
x = [-2 +/- 3*sqr2]/2
So x = [-2 + 3* sqrt2]/2 or x = [-2 - 3*sqr2]/2
Solve 1= (y+3)(2y-2)
Isn't the right side
2y^2 + 4y -6 and not the number you had for the y term?
Ok so now what?
So I looked at your answer and didn't see that what I wrote for the foil on the right is exactly what you have. I get the same final answer as you.
Thank you kind sir
To solve the equation 1 = (y+3)(2y-2), we can use the FOIL method, which stands for First, Outer, Inner, Last.
First, we multiply the first terms of each binomial: y * 2y = 2y^2.
Outer, we multiply the outer terms of each binomial: y * -2 = -2y.
Inner, we multiply the inner terms of each binomial: 3 * 2y = 6y.
Last, we multiply the last terms of each binomial: 3 * -2 = -6.
Putting all the multiplied terms together, we have: 2y^2 - 2y + 6y - 6.
Now, we can combine like terms to simplify the equation: 2y^2 + 4y - 6.
Next, we subtract 1 from both sides to move all the terms to the left side of the equation:
2y^2 + 4y - 6 - 1 = 0.
Simplifying further, we have: 2y^2 + 4y - 7 = 0.
To solve this quadratic equation, we can use the quadratic formula:
y = (-b +/- sqrt(b^2 - 4ac))/(2a),
where a = 2, b = 4, and c = -7.
Substituting these values into the formula, we get:
y = (-4 +/- sqrt(4^2 - 4 * 2 * -7))/(2 * 2).
Simplifying, we have:
y = (-4 +/- sqrt(16 + 56))/(4).
Now, we calculate the value inside the square root:
y = (-4 +/- sqrt(72))/(4).
Since 72 is not a perfect square, we can't simplify the square root any further.
Finally, we can divide each term by 4 to simplify:
y = (-4 +/- 6sqrt(2))/(4).
Simplifying further by dividing each term by 2:
y = (-2 +/- 3sqrt(2))/2.
So, the solutions to the equation are:
y = (-2 + 3sqrt(2))/2,
or
y = (-2 - 3sqrt(2))/2.