Question

Solve the quadratic equation by square roots:

1. 4x²= 81
2. (4x-3)²+7=39

Answer 1

see explanation

Explanation:

(1)

given

4x² = 81 ( divide both sides by 4 )

x² =
`(81)/(4)` ( take the square root of both sides )

x = ±
`\sqrt{(81)/(4) }` = ±
`(9)/(2)`

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(2)

subtract 7 from both sides

(4x - 3)² = 32 ( take the square root of both sides )

4x - 3 = ±
`√(32)` = ± 4
`√(2)`

Add 3 to both sides

4x = 3 ± 4
`√(2)` ( divide both sides by 4 )

x =
`(3)/(4)` ±
`√(2)`