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Solve by completing the square.\newlinet2+26t+41=0t^2 + 26t + 41 = 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+41=0t^2 + 26t + 41 = 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. Rewrite Equation: Rewrite the equation in the form of t2+bt=ct^2 + bt = c.\newlineSubtract 4141 from both sides to set the equation up for completing the square.\newlinet2+26t+41−41=0−41t^2 + 26t + 41 - 41 = 0 - 41\newlinet2+26t=−41t^2 + 26t = -41
  2. Set Up for Completing: Choose the number to add to both sides to complete the square.\newlineSince (262)2=169(\frac{26}{2})^2 = 169, add 169169 to both sides.\newlinet2+26t+169=−41+169t^2 + 26t + 169 = -41 + 169\newlinet2+26t+169=128t^2 + 26t + 169 = 128
  3. Choose Number to Add: Factor the left side of the equation. \newline(t+13)2=128(t + 13)^2 = 128
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(t+13)2=±128\sqrt{(t + 13)^2} = \pm\sqrt{128}\newlinet+13=±128t + 13 = \pm\sqrt{128}
  5. Take Square Root: Simplify the square root of 128128.\newlineSince 128=64×2128 = 64 \times 2 and 64=8\sqrt{64} = 8, we have:\newlinet+13=±82t + 13 = \pm8\sqrt{2}
  6. Simplify Square Root: Isolate the variable tt by subtracting 1313 from both sides.\newlinet+13−13=±82−13t + 13 - 13 = \pm 8\sqrt{2} - 13\newlinet=−13±82t = -13 \pm 8\sqrt{2}
  7. Isolate Variable: Calculate the approximate decimal values of tt.t≈−13+82t \approx -13 + 8\sqrt{2} or t≈−13−82t \approx -13 - 8\sqrt{2}t≈−13+8(1.41)t \approx -13 + 8(1.41) or t≈−13−8(1.41)t \approx -13 - 8(1.41)t≈−13+11.28t \approx -13 + 11.28 or t≈−13−11.28t \approx -13 - 11.28t≈−1.72t \approx -1.72 or t≈−24.28t \approx -24.28

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