My qustion is for the following
the problem reads as follows
(x-1)^2 = 7
x-1=+- sqrt 7
x= 1+- sqrt 7
the method they use was factoring in order to simplify the equation to make it easier is this correc?
x^2-9x-4=6
x^2-9x-10=0
(x-10)(x+1)=0
What method did they use here I think its simplifying but i am not sure?
4x^2-8x+3=5
4x^2-8x-2=0
2(2x^2-4x-1)=0
2x^2-4x-1=0
here the method that they use was first factoring then simplefiying and then they will use the quadratic formula is this correct?
You are right on all counts.
Thank you for your questions.
In the first problem, they used factoring to simplify the equation. They started with the equation (x-1)^2 = 7 and then took the square root of both sides to solve for x. This resulted in x-1 = ±√7. Finally, they added 1 to both sides to isolate x, resulting in x = 1 ± √7. So, in this case, they used factoring to simplify the equation and ultimately solve for x.
In the second problem, they also used factoring to simplify the equation. They started with the equation x^2 - 9x - 4 = 6 and rearranged it to x^2 - 9x - 10 = 0. Then, they factored the quadratic equation into (x-10)(x+1) = 0. By setting each factor equal to zero, they found that x could be either 10 or -1. So, again, they used factoring to simplify the equation and find the solutions for x.
In the third problem, they used a combination of factoring and the quadratic formula. They began with the equation 4x^2 - 8x + 3 = 5 and moved the constant term to the other side, resulting in 4x^2 - 8x - 2 = 0. Then, they factored out a common factor of 2 from the quadratic equation, which gave 2(2x^2 - 4x - 1) = 0. Finally, they used the quadratic formula to find the solutions for 2x^2 - 4x - 1 = 0. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = -4, and c = -1. By substituting these values into the quadratic formula, they could find the solutions for x.
So, you are correct. In the first problem, they used factoring to simplify. In the second problem, they used factoring to simplify and find the solutions. And in the third problem, they used factoring, simplifying, and the quadratic formula to find the solutions.