x² – 35 = 2x
how do I solve this?
Arrange it so all the terms are on the left hand side:
x²-2x-35=0
Factorize, i.e. look for two integers that multiply together will give -35, and when added together will give -2.
-1*35=-35, but -1+35=34, not good
-5*7=-35, but -5+7=+2 (not -2) not good
However, we only have to change the signs to get
5*-7=-35, 5+(-7)=-2 OK
So the factors are:
(x-7)(x+5)=0
THis means either (x-7)=0, or (x+5)=0,
or x=7, or x=-5
-6 = -( x- 5) -3 ( 5+ 2x) -4 (2x -4) solve for x
To solve the equation x² – 35 = 2x, we can use the following steps:
Step 1: Move all the terms to one side of the equation to set it equal to zero. We can do this by subtracting 2x from both sides:
x² – 2x – 35 = 0
Step 2: Now we have a quadratic equation in the standard form ax² + bx + c = 0, where a = 1, b = -2, and c = -35.
Step 3: To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use factoring in this case.
Step 4: Find two numbers whose product is equal to the product of a (1)* c (-35) and whose sum is equal to b (-2). In this case, the numbers are -5 and 7.
Step 5: Rewrite the middle term (-2x) using the two numbers from the previous step:
x² – 5x + 7x – 35 = 0
Step 6: Group the terms and factor by grouping:
(x² – 5x) + (7x – 35) = 0
x(x – 5) + 7(x – 5) = 0
(x + 7)(x – 5) = 0
Step 7: Set each factor equal to zero and solve for x:
x + 7 = 0 or x – 5 = 0
For the first equation,
x = -7
For the second equation,
x = 5
Step 8: Thus, the solutions to the equation x² – 35 = 2x are x = -7 and x = 5.