Question

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answer 1

Explanation:

The steps that Inga can use to solve the quadratic equation 2x^2 + 12x - 3 = 0 are:

Use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 2, b = 12, and c = -3.

Factor out the greatest common factor (GCF) from the quadratic expression: 2(x^2 + 6x - 3/2) = 0. Then, use either the zero product property or divide both sides by the GCF of 2 to solve for x.

Complete the square by adding and subtracting the square of half the coefficient of x from both sides: 2(x + 3)^2 - 27 = 0. Then, isolate the squared term and take the square root of both sides to solve for x.

Answer 2

• 2(x² + 6x) = 3
• 2(x² +6x +9) = 3 +18
• x +3 = ±√(21/2)

Explanation:

You want to know which steps Inga could use to solve the quadratic equation 2x² +12x -3 = 0.

Completing the square

The offered steps are those used to solve the quadratic by completing the square.

2x² +12x = 3 . . . . . . . . . separate the constant from the variable terms

2(x² +6x) = 3 . . . . . . . . . matches choice 3

2(x² +6x +9) = 3 +18 . . . . matches choice 1

2(x +3)² = 21

(x +3)² = 21/2

x +3 = ±√(21/2) . . . . . . . matches choice 4

x = -3 ±√(21/2)

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Additional comment

In the third step above, we have added the square of half the x-coefficient inside parentheses, and an equivalent amount on the other side of the equal sign: (6/2)² = 9, and 2(9) = 18.