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Solve by completing the square.\newlinex2+16x=−35x^2 + 16x = -35\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve by completing the square.\newlinex2+16x=−35x^2 + 16x = -35\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. Rewrite equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c. We have the equation x2+16x=−35x^2 + 16x = -35. To complete the square, we need to move the constant term to the other side of the equation. x2+16x+35=0x^2 + 16x + 35 = 0
  2. Complete the square: Choose the equation after completing the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides of the equation, where bb is the coefficient of xx. In this case, b=16b = 16, so (b/2)2=(16/2)2=82=64(b/2)^2 = (16/2)^2 = 8^2 = 64.\newlinex2+16x+64=35+64x^2 + 16x + 64 = 35 + 64
  3. Factor left side: Identify the equation after factoring the left side.\newlineNow we have a perfect square trinomial on the left side, which factors into (x+8)2(x + 8)^2.\newline(x+8)2=99(x + 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 to solve for xx.\newline(x+8)2=±99\sqrt{(x + 8)^2} = \pm\sqrt{99}\newlinex+8=±99x + 8 = \pm\sqrt{99}
  5. Isolate variable: Choose the equation after isolating the variable xx.\newlineTo isolate xx, subtract 88 from both sides of the equation.\newlinex+8−8=±99−8x + 8 - 8 = \pm\sqrt{99} - 8\newlinex=±99−8x = \pm\sqrt{99} - 8
  6. Calculate values: What are the two values of xx?\newlineNow we need to calculate the square root of 9999 and subtract 88 from it. The square root of 9999 is approximately 9.959.95 (rounded to the nearest hundredth).\newlinex≈9.95−8x \approx 9.95 - 8 or x≈−9.95−8x \approx -9.95 - 8\newlinex≈1.95x \approx 1.95 or x≈−17.95x \approx -17.95

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