Solve the equation 4x^2-12x=7 algebraically for x.

2 answers:

7 0

  4x² - 12x = 7
  - 7 - 7
4x² - 12x - 7 = 0
  4x² + 2x - 14x - 7 = 0
2x(2x) + 2x(1) - 7(2x) - 7(1) = 0
  2x(2x + 1) - 7(2x + 1) = 0
  (2x - 7)(2x + 1) = 0
2x - 7 = 0 or 2x + 1 = 0
+ 7 + 7   - 1 - 1
2x = 7 2x = -1
2 2 2 2
x = 3¹/₂     or     x = ⁻¹/₂

solmaris [256]2 years ago

7 0

First subtract 7 from each side of the equation.

4x^2 - 12x - 7 = 0.

Now we can substitute terms into our friend the quadratic equation, which you should memorize. Or we can try a few simple factors. 7 is prime, so to make -7 one number must be positive and one must be negative.

The first pair I tried, (2x + 1)(2x - 7) yield a middle term of -12x. Therefore, setting each to zero yields: x = -1/2, or x = 7/2.

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