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Question

Difficulty: EasyQuadratic Equations and Factoring

If xx is a negative real number such that x2+5x−14=0x^2 + 5x - 14 = 0, what is the value of x+3x + 3?

  1. A
    −10-10
  2. B
    −7-7
  3. −4-4Answer
  4. D
    22
  5. E
    55

Answer

The value of x+3x + 3 is −4-4.
Factoring x2+5x−14=0x^2 + 5x - 14 = 0 yields (x+7)(x−2)=0(x + 7)(x - 2) = 0, giving solutions x=−7x = -7 and x=2x = 2. Given that xx must be negative, x=−7x = -7. Substituting this into the target expression gives −7+3=−4-7 + 3 = -4.

Step-by-Step Solution

1
Factor the quadratic equation x2+5x−14=0x^2 + 5x - 14 = 0.
(x+7)(x−2)=0(x + 7)(x - 2) = 0
Find two numbers that multiply to −14-14 and add to 55, which are 77 and −2-2.
2
Solve for the possible values of xx.
x=−7x = -7 or x=2x = 2
Set each linear factor equal to zero.
3
Apply the condition that xx is a negative real number.
x=−7x = -7
The value x=2x = 2 is positive and must be discarded.
4
Evaluate the target expression x+3x + 3.
−7+3=−4-7 + 3 = -4
Substitute x=−7x = -7 into x+3x + 3.

Key Concept

Factoring Quadratic Equations and Evaluating Expressions
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Topics

Quadratic Equations and Factoring

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