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Solve by completing the square.\newlinex2+8x=29x^2 + 8x = 29\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+8x=29x^2 + 8x = 29\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. Write Equation Form: Write the equation in the form of x2+bx=cx^2 + bx = c. We have the equation x2+8x=29x^2 + 8x = 29.
  2. Complete Square: Complete the square by adding (b2)2\left(\frac{b}{2}\right)^2 to both sides of the equation.\newlineSince (82)2=16\left(\frac{8}{2}\right)^2=16, we add 1616 to both sides to complete the square.\newlinex2+8x+16=29+16x^2 + 8x + 16 = 29 + 16\newlinex2+8x+16=45x^2 + 8x + 16 = 45
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(x+4)2=45(x + 4)^2 = 45
  4. Take Square Root: Take the square root of both sides of the equation.\newline(x+4)2=±45\sqrt{(x + 4)^2} = \pm\sqrt{45}\newlinex+4=±45x + 4 = \pm\sqrt{45}
  5. Solve for x: Solve for x by isolating the variable.\newlineSubtract 44 from both sides of the equation.\newlinex=4±45x = -4 \pm \sqrt{45}
  6. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.\newline45\sqrt{45} is approximately 6.716.71.\newlinex=4±6.71x = -4 \pm 6.71
  7. Find Values of x: Find the two values of x.\newlinex4+6.71x \approx -4 + 6.71 implies x2.71x \approx 2.71.\newlinex46.71x \approx -4 - 6.71 implies x10.71x \approx -10.71.\newlineValues of x: 2.712.71, 10.71-10.71

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