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Solving the Equation: (x-1)(x+3) = 5
This article will guide you through the steps to solve the equation (x-1)(x+3) = 5.
Step 1: Expand the Equation
First, we need to expand the left-hand side of the equation by multiplying the two binomials:
(x - 1)(x + 3) = x² + 3x - x - 3
Simplifying the expression gives us:
x² + 2x - 3 = 5
Step 2: Move All Terms to One Side
To solve for x, we need to set the equation equal to zero. Subtract 5 from both sides:
x² + 2x - 3 - 5 = 0
This gives us:
x² + 2x - 8 = 0
Step 3: Factor the Quadratic Equation
Now we have a quadratic equation in standard form. We can solve this by factoring.
We need to find two numbers that add up to 2 (the coefficient of the x term) and multiply to -8 (the constant term). The numbers 4 and -2 satisfy these conditions.
Therefore, we can factor the quadratic equation as:
(x + 4)(x - 2) = 0
Step 4: Solve for x
For the product of two terms to be zero, at least one of them must be zero. So we have two possible solutions:
- x + 4 = 0 => x = -4
- x - 2 = 0 => x = 2
Solution
The solutions to the equation (x-1)(x+3) = 5 are x = -4 and x = 2.