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Solve by completing the square.\newlineu2+4u=−1u^2 + 4u = -1\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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Q. Solve by completing the square.\newlineu2+4u=−1u^2 + 4u = -1\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Move Constant Term: Rewrite the equation in the form of u2+bu=cu^2 + bu = c. We have the equation u2+4u=−1u^2 + 4u = -1. To complete the square, we need to move the constant term to the other side. u2+4u+___=−1+___u^2 + 4u + \_\_\_ = -1 + \_\_\_
  2. Find Completing Number: Find the number to complete the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides of the equation. Here, bb is the coefficient of uu, which is 44.\newline(4/2)2=22=4(4/2)^2 = 2^2 = 4\newlineSo, we add 44 to both sides of the equation.\newlineu2+4u+4=−1+4u^2 + 4u + 4 = -1 + 4
  3. Rewrite as Trinomial: Rewrite the equation as a perfect square trinomial.\newlineNow, the left side of the equation is a perfect square trinomial.\newline(u+2)2=3(u + 2)^2 = 3
  4. Solve for u: Solve for u by taking the square root of both sides.\newlineTake the square root of both sides of the equation to solve for u.\newline(u+2)2=±3\sqrt{(u + 2)^2} = \pm\sqrt{3}\newlineu + 22 = \pm\sqrt{33}
  5. Isolate u: Isolate u to find the solutions.\newlineSubtract 22 from both sides to isolate u.\newlineu=−2±3u = -2 \pm \sqrt{3}
  6. Calculate Decimal Values: Calculate the approximate decimal values of uu. Since the question asks for decimals rounded to the nearest hundredth, we calculate the approximate values of 3\sqrt{3}. 3≈1.73\sqrt{3} \approx 1.73 So, u≈−2±1.73u \approx -2 \pm 1.73 u≈−2+1.73u \approx -2 + 1.73 or u≈−2−1.73u \approx -2 - 1.73 u≈−0.27u \approx -0.27 or u≈−3.73u \approx -3.73

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