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Solve by completing the square.\newlinev2+28v+45=0v^2 + 28v + 45 = 0\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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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlinev2+28v+45=0v^2 + 28v + 45 = 0\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. Rewrite Equation: Rewrite the equation in the form of v2+bv=−cv^2 + bv = -c.\newlineSubtract 4545 from both sides.\newlinev2+28v+45−45=0−45v^2 + 28v + 45 - 45 = 0 - 45\newlinev2+28v=−45v^2 + 28v = -45
  2. Complete the Square: Choose the number to add to both sides to complete the square.\newlineSince (282)2=196(\frac{28}{2})^2 = 196, add 196196 to both sides.\newlinev2+28v+196=−45+196v^2 + 28v + 196 = -45 + 196\newlinev2+28v+196=151v^2 + 28v + 196 = 151
  3. Factor Perfect Square: Factor the left side as a perfect square.\newlinev2+28v+196=151v^2 + 28v + 196 = 151\newline(v+14)2=151(v + 14)^2 = 151
  4. Take Square Root: Take the square root of both sides.\newline(v+14)2=±151\sqrt{(v + 14)^2} = \pm\sqrt{151}\newlinev+14=±151v + 14 = \pm\sqrt{151}
  5. Isolate Variable: Isolate the variable vv.\newlineSubtract 1414 from both sides.\newlinev+14−14=±151−14v + 14 - 14 = \pm\sqrt{151} - 14\newlinev=−14±151v = -14 \pm \sqrt{151}
  6. Calculate Approximate Values: Calculate the approximate values of vv.v≈−14+151v \approx -14 + \sqrt{151} and v≈−14−151v \approx -14 - \sqrt{151}v≈−14+12.29v \approx -14 + 12.29 and v≈−14−12.29v \approx -14 - 12.29v≈−1.71v \approx -1.71 and v≈−26.29v \approx -26.29

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