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Solve by completing the square.\newlinex2−28x=−11x^2 - 28x = -11\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.\newlinex2−28x=−11x^2 - 28x = -11\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. Move Constant Term: To complete the square, we need to form a perfect square trinomial on the left side of the equation. We start by moving the constant term to the right side of the equation.\newlinex2−28x+___=−11+___x^2 - 28x + \_\_\_ = -11 + \_\_\_
  2. Find Completing Number: To find the number to complete the square, we take half of the coefficient of xx, which is −28-28, and square it. (−28/2)2=(−14)2=196(-28/2)^2 = (-14)^2 = 196
  3. Add Completing Number: Add 196196 to both sides of the equation to complete the square.\newlinex2−28x+196=−11+196x^2 - 28x + 196 = -11 + 196
  4. Simplify Right Side: Simplify the right side of the equation. x2−28x+196=185x^2 - 28x + 196 = 185
  5. Factor Perfect Square Trinomial: Now we have a perfect square trinomial on the left side, which factors to (x−14)2(x - 14)^2.(x−14)2=185(x - 14)^2 = 185
  6. Take Square Root: Take the square root of both sides of the equation to solve for xx.x−14=±185x - 14 = \pm\sqrt{185}
  7. Isolate xx: Add 1414 to both sides of the equation to isolate xx.x=14±185x = 14 \pm \sqrt{185}
  8. Approximate Square Root: Since 185\sqrt{185} cannot be simplified to an integer or a simple fraction, we can leave it as a square root or approximate it as a decimal.\newline185≈13.60\sqrt{185} \approx 13.60 (rounded to the nearest hundredth)
  9. Write Final Solutions: Write the final solutions, using the approximation for the square root if necessary.\newlinex=14+185x = 14 + \sqrt{185} or x=14−185x = 14 - \sqrt{185}\newlinex≈14+13.60x \approx 14 + 13.60 or x≈14−13.60x \approx 14 - 13.60\newlinex≈27.60x \approx 27.60 or x≈0.40x \approx 0.40

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