Problem
Solve the quadratic equation: 2x² + 7x − 15 = 0
📝Step-by-Step Solution
1
Identify the coefficients
From 2x² + 7x − 15 = 0, we identify: a = 2, b = 7, c = −15
a = 2, b = 7, c = −15
2
Calculate the discriminant
Δ = b² − 4ac = (7)² − 4(2)(−15) = 49 + 120 = 169
Δ = 49 + 120 = 169
3
Apply the quadratic formula
x = (−b ± √Δ) / 2a = (−7 ± √169) / 2(2) = (−7 ± 13) / 4
x = (−7 ± 13) / 4
4
Calculate both solutions
x₁ = (−7 + 13) / 4 = 6/4 = 3/2 = 1.5. x₂ = (−7 − 13) / 4 = −20/4 = −5
x₁ = 1.5, x₂ = −5
✅Final Answer
x = 1.5 or x = −5
The discriminant Δ = 169 = 13² is a perfect square, which means the solutions are rational numbers. When a ≠ 1, remember to divide by 2a (which is 4 here), not just 2.
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