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10w^(2)+45 w=7

10w2+45w=7 10 w^{2}+45 w=7

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Full solution

Q. 10w2+45w=7 10 w^{2}+45 w=7
  1. Move to one side: First, let's move everything to one side to set the equation to zero.\newline10w2+45w−7=010w^2 + 45w - 7 = 0
  2. Factor or use formula: Now, we need to factor this quadratic equation, but it doesn't factor nicely. So, let's use the quadratic formula instead.\newlinew=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\newlineHere, a=10a = 10, b=45b = 45, and c=−7c = -7.
  3. Plug values into formula: Plug the values into the quadratic formula.\newlinew=−(45)±(45)2−4(10)(−7)2(10)w = \frac{-\left(45\right) \pm \sqrt{\left(45\right)^2 - 4\left(10\right)\left(-7\right)}}{2\left(10\right)}
  4. Simplify square root: Simplify inside the square root. w=−45±2025+28020w = \frac{{-45 \pm \sqrt{{2025 + 280}}}}{20}
  5. Add solutions: Add up the numbers under the square root. \newlinew=−45±230520w = \frac{-45 \pm \sqrt{2305}}{20}
  6. Add solutions: Add up the numbers under the square root.\newlinew=−45±230520w = \frac{-45 \pm \sqrt{2305}}{20}Now, let's simplify the square root. But wait, 23052305 isn't a perfect square, so we can't simplify it further. We'll just leave it under the square root.\newlinew=−45±230520w = \frac{-45 \pm \sqrt{2305}}{20}
  7. Add solutions: Add up the numbers under the square root.\newlinew=−45±230520w = \frac{-45 \pm \sqrt{2305}}{20}Now, let's simplify the square root. But wait, 23052305 isn't a perfect square, so we can't simplify it further. We'll just leave it under the square root.\newlinew=−45±230520w = \frac{-45 \pm \sqrt{2305}}{20}So, we have two solutions for ww, one with the plus and one with the minus.\newlinew1=−45+230520w_1 = \frac{-45 + \sqrt{2305}}{20}\newlinew2=−45−230520w_2 = \frac{-45 - \sqrt{2305}}{20}

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