Question

now fill in the correct values. be extra careful with the signs. take note of what signs are already given to you. $8x^2 + 14x + 5 = 0$ $x = \frac{-(\square)\pm\sqrt{(\square)^2 - \square(\square)(\square)}}{\square(\square)}$

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula for a quadratic equation \(ax^2 + bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).

Step2: Identify \(a\), \(b\), \(c\)

For the equation \(8x^2 + 14x + 5 = 0\), we have \(a = 8\), \(b = 14\), \(c = 5\).

Step3: Substitute into Formula

Substitute \(a = 8\), \(b = 14\), \(c = 5\) into the quadratic formula. So we get \(x=\frac{-(14)\pm\sqrt{(14)^2 - 4(8)(5)}}{2(8)}\).

Answer:

In the numerator's first box: \(14\), the square - root box: \(14\), the exponent box: \(2\), the coefficient of the middle term in the discriminant: \(4\), the next two boxes: \(8\) and \(5\) respectively, and in the denominator: \(2\) and \(8\) respectively. So filling in the blanks we have \(x=\frac{-(14)\pm\sqrt{(14)^{2}-4(8)(5)}}{2(8)}\)