Write each equation in standard form (set equal to zero). Then solve by factoring.
Example:
x²-2x=8
X^2 -2X = 8
In "set to zero" form:
X^2 - 2X - 8 = 0
factoring:
(X + ?) * (X + ?) = 0
The two different numbers that are question marks must equal 8 when multiplying them together. This would suggest trying:
1, 8
or 2, 4
Since 8 is negative, one of the values must be negative.
The first factor is:
(X - 4)
So...
(X - 4) * (X + ?)
You can get the second factor easily from that.
To write the equation in standard form, we need to set it equal to zero. So, let's subtract 8 from both sides:
x² - 2x - 8 = 0
Now, let's solve it by factoring.
To factor this quadratic equation, we need to find two numbers whose sum is -2 (the coefficient of the x term) and whose product is -8 (the constant term). The numbers that satisfy these conditions are -4 and 2.
So, we can rewrite the equation as:
(x - 4)(x + 2) = 0
Now, to solve for x, we set each factor equal to zero:
x - 4 = 0 or x + 2 = 0
Solving these equations will give us the solutions:
For x - 4 = 0, adding 4 to both sides gives us x = 4.
For x + 2 = 0, subtracting 2 from both sides gives us x = -2.
Therefore, the solutions to the equation x² - 2x = 8 are x = 4 and x = -2.
To write the equation in standard form (set equal to zero), we need to move all the terms to one side of the equation.
Given the equation x²-2x=8, we can begin by subtracting 8 from both sides:
x²-2x-8=0
Now that the equation is in standard form, we can try to solve it by factoring.
To factor the equation x²-2x-8, we need to find two numbers that, when multiplied, equal -8, and when added, equal -2. These numbers are -4 and 2, since (-4) * (2) = -8 and (-4) + (2) = -2.
Using these numbers, we can rewrite the equation using factoring:
(x - 4)(x + 2) = 0
To solve for x, we can set each factor equal to zero and solve for x separately:
x - 4 = 0 --> x = 4
x + 2 = 0 --> x = -2
Therefore, the solutions to the equation x²-2x=8 are x = 4 and x = -2.