Question

which equation shows the quadratic formula used correctly to solve (7x^2 = 9 + x) for (x)?

(x = \frac{-1 \pm \sqrt{(1)^2 - 4(7)(9)}}{2(7)})

(x = \frac{1 \pm \sqrt{(-1)^2 - 4(7)(9)}}{2(7)})

(x = \frac{-1 \pm \sqrt{(-1)^2 + 4(7)(9)}}{2(7)})

(x = \frac{1 \pm \sqrt{(-1)^2 + 4(7)(9)}}{2(7)})

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Standard Form

$$ 7x^2 - x - 9 = 0 $$

Step 2: Identify Coefficients

$$ a = 7, \quad b = -1, \quad c = -9 $$

Step 3: Substitute into Quadratic Formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(7)(-9)}}{2(7)} $$

$$ x = \frac{1 \pm \sqrt{(-1)^2 + 4(7)(9)}}{2(7)} $$

Answer:

The correct equation is the fourth option:

$$ x = \frac{1 \pm \sqrt{(-1)^2 + 4(7)(9)}}{2(7)} $$