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Solve by completing the square.\newlinet2−26t+45=0t^2 - 26t + 45 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____

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Q. Solve by completing the square.\newlinet2−26t+45=0t^2 - 26t + 45 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____
  1. Write Equation Form: Write the equation in the form of t2+bt=ct^2 + bt = c. The given equation is already in this form: t2−26t+45=0t^2 - 26t + 45 = 0.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineSubtract 4545 from both sides to isolate the t2t^2 and tt terms.\newlinet2−26t=−45t^2 - 26t = -45
  3. Find Completing Square Number: Find the number to add to both sides to complete the square.\newlineTake half of the coefficient of tt, square it, and add it to both sides.\newline(−26/2)2=(−13)2=169(-26/2)^2 = (-13)^2 = 169\newlinet2−26t+169=−45+169t^2 − 26t + 169 = -45 + 169
  4. Write Perfect Square Trinomial: Write the left side as a perfect square trinomial and simplify the right side.\newlinet2−26t+169=124t^2 - 26t + 169 = 124\newline(t−13)2=124(t - 13)^2 = 124
  5. Take Square Root: Take the square root of both sides of the equation.\newline(t−13)2=±124\sqrt{(t - 13)^2} = \pm\sqrt{124}\newlinet−13=±124t - 13 = \pm\sqrt{124}
  6. Solve for t: Solve for t by adding 1313 to both sides of the equation.\newlinet=13±124t = 13 \pm \sqrt{124}\newlineSince 124\sqrt{124} is approximately 1111.1414, we can write:\newlinet≈13+11.14t \approx 13 + 11.14 or t≈13−11.14t \approx 13 - 11.14\newlinet≈24.14t \approx 24.14 or t≈1.86t \approx 1.86

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