Solve using the quadratic formula.5y2−6y−4=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Q. Solve using the quadratic formula.5y2−6y−4=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation5y2−6y−4=0. Comparing 5y2−6y−4=0 with the standard form ax2+bx+c=0, we find: a=5b=−6c=−4
Substitute values: Substitute the values of a, b, and c into the quadratic formula y=2a−b±b2−4ac.The quadratic formula is y=2⋅5−(−6)±(−6)2−4⋅5⋅(−4).
Simplify expression: Simplify the expression inside the square root and the constants outside the square root.Calculate the discriminant: b2−4ac=(−6)2−4⋅5⋅(−4)=36+80=116.Then, the quadratic formula becomes y=106±116.
Calculate solutions: Simplify the square root of 116.Since 116 is not a perfect square, we will leave it as 116 for now.The quadratic formula now is y=106±116.
Round values: Calculate the two possible solutions for y.First solution: y=106+116.Second solution: y=106−116.
Round values: Calculate the two possible solutions for y. First solution: y=106+116. Second solution: y=106−116. Round the values of y to the nearest hundredth, if required. First, we calculate the approximate values of 116 which is approximately 10.77. Then, we have y≈106+10.77 or y≈106−10.77. y≈1016.77 or y≈10−4.77. y=106+1160 or y=106+1161.
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