Question

4x²-4x-7=0 ,solve the quadratic function.​

Answer 1

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$4 {x}^{2} - 4x - 7 = 0 \\ a = 4 \\ b = - 4 \\ c = - 7 \\ \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 4)± \sqrt{ {( - 4)}^{2} - 4 \times 4 \times ( - 7) } }{2 \times 4} \\ x = \frac{4± \sqrt{16 - ( - 112)} }{8} \\ x = \frac{4± \sqrt{16 + 112} }{8} \\ x = \frac{4± \sqrt{128} }{8} \\ x = \frac{4± \sqrt{64 \times 2} }{8} \\ x = \frac{4± \sqrt{ {8}^{2} \times 2 } }{8} \\ x = \frac{4±8 \sqrt{2} }{8} \\ x = \frac{4 + 8 \sqrt{2} }{8} \: \: \: or \: \: \: \frac{4 - 8 \sqrt{2} }{8} \\ x = \frac{12 \sqrt{2} }{8} \: \: \: or \: \: \: \frac{ - 4 \sqrt{2} }{8} \\ \large{ \boxed{x = \underline{ \underline{\frac{3 \sqrt{2} }{2} }} \: \: \: or \: \: \: \underline{ \underline{\frac{ - 1 \sqrt{2} }{2} }}}}$