Solve the equation $5 x^{2}+8 x-23=0$
Show your working clearly.
Give your solutions correct to 3 significant figures.
What is the positive solution?

Answer

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Answer

$\boxed{x \approx 1.489}$ is the positive solution

Steps

Step 1 ：Given the quadratic equation: $5x^2 + 8x - 23 = 0$

Step 2 ：Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Step 3 ：Substitute the values: $a = 5$, $b = 8$, and $c = -23$

Step 4 ：Calculate the discriminant: $\Delta = b^2 - 4ac = 524$

Step 5 ：Find the two possible solutions for x: $x_1 = \frac{-8 + \sqrt{524}}{10}$ and $x_2 = \frac{-8 - \sqrt{524}}{10}$

Step 6 ：Calculate the values of $x_1$ and $x_2$: $x_1 \approx 1.489$ and $x_2 \approx -3.089$

Step 7 ：$\boxed{x \approx 1.489}$ is the positive solution