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Solve using the quadratic formula.\newline4x2+4x+1=04x^2 + 4x + 1 = 0\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 using the quadratic formula.\newline4x2+4x+1=04x^2 + 4x + 1 = 0\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. Identify coefficients: Identify the coefficients of the quadratic equation 4x2+4x+1=04x^2 + 4x + 1 = 0. The coefficients are a=4a = 4, b=4b = 4, and c=1c = 1.
  2. Recall quadratic formula: Recall the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of xx.
  3. Substitute coefficients: Substitute the coefficients aa, bb, and cc into the quadratic formula.x=−(4)±(4)2−4(4)(1)2(4)x = \frac{{-(4) \pm \sqrt{{(4)^2 - 4(4)(1)}}}}{{2(4)}}
  4. Simplify expression: Simplify the expression under the square root (the discriminant).\newlinex=−4±16−168x = \frac{{-4 \pm \sqrt{{16 - 16}}}}{8}
  5. Calculate discriminant: Calculate the discriminant.\newline16−16=016 - 16 = 0\newlineSo, the expression under the square root is 00.\newlinex=(−4±0)/8x = (-4 \pm \sqrt{0}) / 8
  6. Simplify further: Since the square root of 00 is 00, simplify the equation further.x=−4±08x = \frac{{-4 \pm 0}}{{8}}
  7. Solve for x: Solve for x by splitting the equation into the two possible solutions with the ±\pm sign.\newlineSince the square root of 00 is 00, there is only one solution in this case.\newlinex=(−4+0)/8x = (-4 + 0) / 8 or x=(−4−0)/8x = (-4 - 0) / 8
  8. Simplify expressions: Simplify both expressions to find the value of xx.x=−48x = \frac{-4}{8} or x=−48x = \frac{-4}{8}
  9. Reduce fractions: Reduce the fraction to its simplest form. x=−12x = -\frac{1}{2} or x=−12x = -\frac{1}{2}

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