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Solve by completing the square.\newlinep2+16p=35p^2 + 16p = 35\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____

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Q. Solve by completing the square.\newlinep2+16p=35p^2 + 16p = 35\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____
  1. Rewrite Equation: Rewrite the equation in the form of p2+bp=cp^2 + bp = c.\newlineSubtract 3535 from both sides to set the equation to zero.\newlinep2+16p−35=0p^2 + 16p - 35 = 0
  2. Complete the Square: Choose the equation after completing the square.\newlineSince (162)2=64(\frac{16}{2})^2 = 64, add 6464 to both sides to complete the square.\newlinep2+16p+64=35+64p^2 + 16p + 64 = 35 + 64\newlinep2+16p+64=99p^2 + 16p + 64 = 99
  3. Factor Left Side: Identify the equation after factoring the left side.\newline(p+8)2=99(p + 8)^2 = 99
  4. Take Square Root: Identify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(p+8)2=±99\sqrt{(p + 8)^2} = \pm\sqrt{99}\newlinep + 88 = ±99\pm\sqrt{99}
  5. Isolate Variable: Choose the equation after isolating the variable pp. To isolate pp, subtract 88 from both sides of the equation. p+8−8=±99−8p + 8 - 8 = \pm\sqrt{99} - 8 p=−8±99p = -8 \pm\sqrt{99}
  6. Calculate Approximate Values: Calculate the approximate values of pp, rounding to the nearest hundredth.p≈−8+99p \approx -8 + \sqrt{99} or p≈−8−99p \approx -8 - \sqrt{99}p≈−8+9.95p \approx -8 + 9.95 or p≈−8−9.95p \approx -8 - 9.95p≈1.95p \approx 1.95 or p≈−17.95p \approx -17.95

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