Question

lets simplify.
8x² + 14x + 5 = 0
x = (□ ± √(□ - □)) / □

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(8x^{2}+14x + 5 = 0\), we identify \(a = 8\), \(b = 14\), and \(c = 5\).

Step2: Substitute Values into Formula

• The numerator's first term (before \(\pm\)) is \(-b\), so substituting \(b = 14\), we get \(- 14\).
• The term inside the square root (the first box under the square root) is \(b^{2}\), so \(b^{2}=14^{2}=196\).
• The term subtracted inside the square root is \(4ac\), so \(4ac = 4\times8\times5=160\).
• The denominator is \(2a\), so \(2a = 2\times8 = 16\).

Answer:

\(x=\frac{-14\pm\sqrt{196 - 160}}{16}\) (So the boxes are filled with \(-14\), \(196\), \(160\), and \(16\) respectively in the order of the numerator's first term, the term under the square root first, the term subtracted under the square root, and the denominator).