2x^2-12x+32=x^2 how would I solve this by factoring?
2x^2-12x+32=x^2
x^2 - 12x + 32 = 0
(x-8)(x-4) = 0
x = 8 or x = 4
2x^2 - 12x + 32 = x^2
Move x^2 to the left side and change sign then put zero after equal sign..
2x^2 - x^2 - 12x + 32 = 0
x^2 - 12x + 32 = 0
(x - 4)(x - 8) = 0
x - 4 = 0 x - 8 = 0
x - 4 + 4 = 0 + 4 x - 8 + 8 = 0 + 8
x = 4 x = 8
x = 4,8
To solve the equation 2x^2 - 12x + 32 = x^2 by factoring, you can follow these steps:
Step 1: Move all the terms to one side of the equation to set it equal to zero:
2x^2 - 12x + 32 - x^2 = 0
Step 2: Combine like terms on the left side of the equation:
x^2 - 12x + 32 = 0
Step 3: Factor the quadratic expression on the left side:
(x - 4)(x - 8) = 0
Here's how you can factor it:
To factor the quadratic expression x^2 - 12x + 32, you need to find two numbers that multiply together to give you the constant term (32) and add up to give you the coefficient of the x term (-12).
The constant term (32) has several factors: 1, 2, 4, 8, 16, and 32.
Next, you need to find two numbers among these factors that add up to -12. In this case, the numbers are -4 and -8 since -4 * -8 = 32 and -4 + -8 = -12.
Now, split the middle term -12x into -4x and -8x:
x^2 - 4x - 8x + 32 = 0
Step 4: Factor by grouping:
(x^2 - 4x) + (-8x + 32) = 0
Factor out the greatest common factor from the first two terms and the last two terms:
x(x - 4) - 8(x - 4) = 0
Now, notice that (x - 4) is a common factor in both terms, so you can factor it out:
(x - 4)(x - 8) = 0
Step 5: Apply the zero product property:
For the equation to be true, either (x - 4) must equal zero or (x - 8) must equal zero.
Therefore, set each factor equal to zero and solve for x:
x - 4 = 0 -> x = 4
x - 8 = 0 -> x = 8
So the solutions to the equation 2x^2 - 12x + 32 = x^2 are x = 4 and x = 8.