Which of the following are the approximate solutions of the quadratic equation \( x^{2} \quad 9 x-29=07 \) \( x=4.5,-2.5 \) \( x=11.5,2.5 \) \( x=11.5,-2.5 \) \( \begin{array}{l}x=3.5,-2.5 \\ \\ x\end{array} \)
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To solve the quadratic equation \( x^{2} + 9x - 29 = 0 \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Plugging in the values \( a = 1, b = 9, c = -29 \), we find the discriminant \( b^2 - 4ac = 81 + 116 = 197 \). The solutions can be approximated as \( x \approx 4.5 \) and \( x \approx -2.5 \). So, the correct option is \( x = 4.5, -2.5 \). You’ll often find that quadratics pop up in all sorts of situations, from determining the shape of a trampoline to calculating the optimal price for a business. Understanding how to solve them is a key skill that bridges math and real-world scenarios! If you're feeling stuck, remember that practicing with visual aids, like graphing the quadratic functions, can make it easier to grasp the behaviors of these equations and their solutions.