Solve the equation using the quadratic formula:
\[ x^2 - 10x + 25 = 18 \]
Answer (2)
x 2 − 10 x + 25 = 18 x 2 − 10 x + 25 − 18 = 0 x 2 − 10 x + 7 = 0 a = 1 , b = − 10 , c = 7 Δ = b 2 − 4 a c = ( − 10 ) 2 − 4 ∗ 1 ∗ 7 = 100 − 28 = 72 Δ = 72 = 2 ∗ 36 = 36 ∗ 2 = 6 2
x 1 = 2 a − b − Δ = 2 10 − 6 2 = 2 2 ( 5 − 3 2 ) = 5 − 3 2 x 2 = 2 a − b + Δ = 2 10 + 6 2 = 2 2 ( 5 + 3 2 ) = 5 + 3 2
A n s w er : x = 5 − 3 2 or x = 5 + 3 2
To solve the equation x 2 − 10 x + 25 = 18 , we rearrange it to x 2 − 10 x + 7 = 0 . Using the quadratic formula, we find the solutions to be x = 5 − 3 2 and x = 5 + 3 2 .
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