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Solve using the quadratic formula.\newline4y2+7y2=04y^2 + 7y - 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve using the quadratic formula.\newline4y2+7y2=04y^2 + 7y - 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 4y2+7y2=04y^2 + 7y - 2 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.\newlinea=4a = 4, b=7b = 7, c=2c = -2
  2. Write quadratic formula: Write down the quadratic formula, which is y=b±b24ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.\newliney=(7)±(7)24(4)(2)2(4)y = \frac{{-(-7) \pm \sqrt{{(7)^2 - 4(4)(-2)}}}}{{2(4)}}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (7)24(4)(2)=49+32=81\sqrt{(7)^2 - 4(4)(-2)} = \sqrt{49 + 32} = \sqrt{81}
  5. Calculate square root: Calculate the square root of the discriminant. 81=9\sqrt{81} = 9
  6. Insert square root: Insert the value of the square root back into the quadratic formula.\newliney = (7±9)/8(-7 \pm \sqrt{9}) / 8
  7. Calculate solutions: Calculate the two possible solutions for yy.y=7+98y = \frac{{-7 + 9}}{{8}} or y=798y = \frac{{-7 - 9}}{{8}}y=28y = \frac{{2}}{{8}} or y=168y = \frac{{-16}}{{8}}
  8. Simplify fractions: Simplify the fractions to get the solutions in simplest form. y=14y = \frac{1}{4} or y=2y = -2
  9. Round non-integer: If necessary, round the non-integer solution to the nearest hundredth.\newlineSince 14\frac{1}{4} is already in simplest form and is a proper fraction, no rounding is needed.

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