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Solve the equation x^(2)-7x+8=0 to the nearest tenth. Answer: x=

Solve the equation x2−7x+8=0 x^{2}-7 x+8=0 to the nearest tenth.\newlineAnswer: x= x=

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Q. Solve the equation x2−7x+8=0 x^{2}-7 x+8=0 to the nearest tenth.\newlineAnswer: x= x=
  1. Identify Equation Type: Identify the type of equation.\newlineWe have a quadratic equation in the form of ax2+bx+c=0ax^2 + bx + c = 0, where a=1a = 1, b=−7b = -7, and c=8c = 8.
  2. Solve Using Quadratic Formula: Solve the quadratic equation using the quadratic formula.\newlineThe quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineHere, a=1a = 1, b=−7b = -7, and c=8c = 8.
  3. Calculate Discriminant: Calculate the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = (−7)2−4(1)(8)=49−32=17(-7)^2 - 4(1)(8) = 49 - 32 = 17.
  4. Apply to Quadratic Formula: Apply the discriminant to the quadratic formula.\newlinex=−(−7)±172⋅1x = \frac{-(-7) \pm \sqrt{17}}{2 \cdot 1}\newlinex=7±172x = \frac{7 \pm \sqrt{17}}{2}
  5. Calculate Possible Solutions: Calculate the two possible solutions for xx.\newlineFirst solution: x=7+172x = \frac{7 + \sqrt{17}}{2}\newlineSecond solution: x=7−172x = \frac{7 - \sqrt{17}}{2}
  6. Evaluate Solutions: Evaluate the solutions to the nearest tenth.\newlineFirst solution: x≈(7+4.123)/2≈11.123/2≈5.6x \approx (7 + 4.123) / 2 \approx 11.123 / 2 \approx 5.6\newlineSecond solution: x≈(7−4.123)/2≈2.877/2≈1.4x \approx (7 - 4.123) / 2 \approx 2.877 / 2 \approx 1.4

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