for what values of x is $x^2 + 2x = 24$ true?\n-6 and -4\n-4 and 6\n4 and -6\n6 and 4

for what values of x is $x^2 + 2x = 24$ true?\n-6 and -4\n-4 and 6\n4 and -6\n6 and 4

for what values of x is $x^2 + 2x = 24$ true?\n-6 and -4\n-4 and 6\n4 and -6\n6 and 4

Answer

Explanation:

Step1: Rearrange the equation

First, we rearrange the given equation (x^{2}+2x = 24) into standard quadratic form (ax^{2}+bx + c=0). Subtract 24 from both sides: (x^{2}+2x - 24=0)

Step2: Factor the quadratic

We need to factor (x^{2}+2x - 24). We look for two numbers that multiply to (- 24) and add up to (2). The numbers are (6) and (-4) because (6\times(-4)=-24) and (6 + (-4)=2). So, the factored form is: ((x + 6)(x - 4)=0)

Step3: Solve for x

Using the zero - product property, if (ab = 0), then either (a = 0) or (b = 0).

  • If (x+6 = 0), then (x=-6).
  • If (x - 4=0), then (x = 4).

Answer:

4 and -6 (the third option: 4 and -6)