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Jan 20

To solve the quadratic equation x^2 + 13x + 42 = 0, we can use factoring or the quadratic formula.

Factoring:

We need to find two numbers that multiply to give 42 and add up to 13. The numbers are 6 and 7.

Therefore, we can rewrite the equation as (x + 6)(x + 7) = 0.

Setting each factor equal to zero, we have x + 6 = 0 and x + 7 = 0.

Solving for x, we find x = -6 and x = -7.

Quadratic formula:

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 1, b = 13, and c = 42.

Plugging these values into the formula, we have x = (-13 ± √(13^2 - 4(1)(42))) / (2(1)).

Simplifying further, we have x = (-13 ± √(169 - 168)) / 2.

x = (-13 ± √1) / 2.

x = (-13 ± 1) / 2.

This gives us two solutions: x = (-13 + 1) / 2 = -6 and x = (-13 - 1) / 2 = -7.

Therefore, the solutions to the quadratic equation x^2 + 13x + 42 = 0 are x = -6 and x = -7.

Factoring:

We need to find two numbers that multiply to give 42 and add up to 13. The numbers are 6 and 7.

Therefore, we can rewrite the equation as (x + 6)(x + 7) = 0.

Setting each factor equal to zero, we have x + 6 = 0 and x + 7 = 0.

Solving for x, we find x = -6 and x = -7.

Quadratic formula:

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 1, b = 13, and c = 42.

Plugging these values into the formula, we have x = (-13 ± √(13^2 - 4(1)(42))) / (2(1)).

Simplifying further, we have x = (-13 ± √(169 - 168)) / 2.

x = (-13 ± √1) / 2.

x = (-13 ± 1) / 2.

This gives us two solutions: x = (-13 + 1) / 2 = -6 and x = (-13 - 1) / 2 = -7.

Therefore, the solutions to the quadratic equation x^2 + 13x + 42 = 0 are x = -6 and x = -7.

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