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Use the quadratic formula to solve. Express your answer in simplest form. q^(2)+10 q+25=0 Answer: q=

Use the quadratic formula to solve. Express your answer in simplest form.\newlineq2+10q+25=0 q^{2}+10 q+25=0 \newlineAnswer: q= q=

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Full solution

Q. Use the quadratic formula to solve. Express your answer in simplest form.\newlineq2+10q+25=0 q^{2}+10 q+25=0 \newlineAnswer: q= q=
  1. Quadratic Formula: The quadratic formula is given by q=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=1a = 1, b=10b = 10, and c=25c = 25.
  2. Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is 102−4(1)(25)10^2 - 4(1)(25).
  3. Discriminant Calculation: Calculating the discriminant: 102−4(1)(25)=100−100=010^2 - 4(1)(25) = 100 - 100 = 0.
  4. Apply Quadratic Formula: Since the discriminant is 00, the equation has one real root (a repeated root). We can now apply the quadratic formula with the discriminant: q=−b±(0)2aq = \frac{-b \pm \sqrt{(0)}}{2a}.
  5. Plug in Values: Plugging in the values of aa and bb into the formula: q=(−10±(0)2⋅1)q = (\frac{-10 \pm \sqrt{(0)}}{2\cdot1}).
  6. Simplify Expression: Simplifying the expression: q=−10±02=−102q = \frac{-10 \pm 0}{2} = \frac{-10}{2}.
  7. Final Solution: The final solution is q=−5q = -5. Since the discriminant was 00, this is the only solution.

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