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Solve by completing the square.\newlinev2+30v=49v^2 + 30v = 49\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____

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Q. Solve by completing the square.\newlinev2+30v=49v^2 + 30v = 49\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____
  1. Write Equation Form: Write the equation in the form of v2+bv=cv^2 + bv = c. The given equation is already in this form: v2+30v=49v^2 + 30v = 49.
  2. Complete Square: Complete the square by adding (b/2)2(b/2)^2 to both sides of the equation.\newlineSince (30/2)2=225(30/2)^2 = 225, add 225225 to both sides to complete the square.\newlinev2+30v+225=49+225v^2 + 30v + 225 = 49 + 225\newlinev2+30v+225=274v^2 + 30v + 225 = 274
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(v+15)2=274(v + 15)^2 = 274
  4. Take Square Root: Take the square root of both sides of the equation.\newline(v+15)2=±274\sqrt{(v + 15)^2} = \pm\sqrt{274}\newlinev+15=±274v + 15 = \pm\sqrt{274}
  5. Solve for vv: Solve for vv by isolating the variable.\newlineSubtract 1515 from both sides of the equation.\newlinev=−15±274v = -15 \pm \sqrt{274}
  6. Calculate Decimal Values: Calculate the approximate decimal values of vv.274\sqrt{274} is approximately 16.5516.55 (rounded to the nearest hundredth).v≈−15+16.55v \approx -15 + 16.55 or v≈−15−16.55v \approx -15 - 16.55v≈1.55v \approx 1.55 or v≈−31.55v \approx -31.55

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