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Problem:
Solve for x: 2x² - 7x - 15 = 0
Step 1: Identify the coefficients
In the quadratic equation 2x² - 7x - 15 = 0:
a = 2, b = -7, c = -15
Step 2: Try to factor the equation
We need to find two numbers that multiply to give 2 × (-15) = -30 and add up to -7.
The numbers are 3 and -10, since 3 × (-10) = -30 and 3 + (-10) = -7.
Step 3: Rewrite the equation in factored form
2x² - 7x - 15 = 0
(2x + 3)(x - 5) = 0
Step 4: Set each factor equal to zero and solve
2x + 3 = 0 → x = -3/2
x - 5 = 0 → x = 5
Solution:
x = -3/2 or x = 5
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