Question

Solve the equation 0 = x^2 + 4x − 6 for exact values.

Answer 1

Answer:

x = -2 ± √10

Step-by-step explanation:

x^2 + 4x − 6 = 0

Method I - Solve by completing the square

Add 6 to both sides

x^2 + 4x = 6

use half the x coefficient (4/2 = 2) as the complete the square term.

(x + 2)² = 6 + 2²

(x + 2)² = 10

Take the square root of both sides

x + 2 = ±√10

subtract 2 from both sides

x = -2 ± √10

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M ethod II - Quadratic equation

x = [ -b ± √(b² - 4ac) ]  /  (2a)

x = [ -4 ± √ (4² - 4(1)(-6)) ] / 2

x = [ -4 ± √ (16 + 24) ] / 2

x = [ -4 ± √40 ] / 2

x = [ -4 ± √(4 * 10) ] / 2

x = [ -4 ± 2√10 ] / 2

x = -2 ± √10