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Let’s check out your problem:

x^(2)+16 x+5=0

x2+16x+5=0 x^{2}+16 x+5=0

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Full solution

Q. x2+16x+5=0 x^{2}+16 x+5=0
  1. Factor Quadratic Equation: First, let's try to factor the quadratic equation x2+16x+5=0x^2 + 16x + 5 = 0. We look for two numbers that multiply to 55 and add up to 1616.
  2. Use Quadratic Formula: Hmm, it's kinda hard to find integers that do that. Let's use the quadratic formula instead.\newlineThe quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=16b = 16, and c=5c = 5.
  3. Plug Values into Formula: Plug the values into the formula: x=−(16)±(16)2−4⋅1⋅52⋅1x = \frac{{-\left(16\right) \pm \sqrt{{\left(16\right)^2 - 4\cdot 1\cdot 5}}}}{{2\cdot 1}}.
  4. Calculate Square Root: Calculate inside the square root: 256−20=236\sqrt{256 - 20} = \sqrt{236}.
  5. Simplify Square Root: Now we have x=−16±2362x = \frac{{-16 \pm \sqrt{236}}}{2}.
  6. Find Solutions: Simplify the square root if possible. 236\sqrt{236} can't be simplified nicely, so we leave it like that.
  7. Find Solutions: Simplify the square root if possible. 236\sqrt{236} can't be simplified nicely, so we leave it like that.So the solutions are x=−16+2362x = \frac{-16 + \sqrt{236}}{2} and x=−16−2362x = \frac{-16 - \sqrt{236}}{2}.

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