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(2x² + 7x - 15) + (x + 5)

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We are given the below expression


\begin{gathered} (4x^2\text{ + x + 1) + (x - 2)} \\ \text{First, open the parentheses} \\ 4x^2\text{ + x + 1 + x - 2} \\ \text{Collect the like terms} \\ 4x^2\text{ + x + x + 1 - 2} \\ 4x^2\text{ + 2x - 1} \end{gathered}

From the quadratic function generated, we will be solving for x using the general formula


\begin{gathered} ax^2\text{ + bx + c = 0} \\ 4x^2\text{ + 2x - 1= 0} \\ \text{let a = 4, b= 2 and c = -1} \\ \text{The general quadratic formula is written as} \\ x\text{ = -b }\pm\text{ }\frac{\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{Substitute the above values into the formula} \\ x\text{ = -(2) }\pm\text{ }\frac{\sqrt[]{2^2\text{ - 4 x 4(-1)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ -4(-4)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ + 16}}}{8} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{20}}{8} \\ \sqrt[]{20}\text{ = }\sqrt[]{4}\text{ x }\sqrt[]{5} \\ \sqrt[]{20\text{ }}\text{ = 2}\sqrt[]{5} \\ \text{Hence,} \\ x\text{ = -2 + }\frac{2\sqrt[]{5}}{8}\text{ OR -2 - }\frac{2\sqrt[]{5}}{8} \\ x\text{ = 0.3090 or x = -0.8075} \end{gathered}

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