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Solve using quadratic formula x2 – 4x + 3 = 0

Solve using quadratic formula x2 – 4x + 3 = 0

Answer

x = 3,1

Solution

x² – 4x + 3 = 0

Use the quadratic formula to find the solutions.

-b ± √b² – 4(ac) ÷ 2a

Substitute the values a = 1, b = -4, and c = 3 into the quadratic formula and solve for x.

4 ± √(-4)² – 4(1 X 3) ÷ 2 X 1

Simplify the numerator

Raise -4 to the power of 2.

x = 4 ± √16 – 4 X 3 ÷ 2

Multiply -4 by 3

x = 4 ± √16 – 12 ÷ 2

Subtract 12 from 16

x = 4 ± √4 ÷ 2

Rewrite 4 as 2²

x = 4 ± √2² ÷ 2

Pull terms out from under the radical, assuming positive real numbers.

x = 4 ± 2 ÷ 2

Simplify x = 4 ± 2 ÷2

x = 2 ± 1

x = 2 + 1 or x = 2 – 1

x = 3 or x = 1

The final answer is the combination of both solutions.

x = 3,1

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