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9 Marina starts to solve the quadratic equation 3x^2+5x-2=0 3x^2+5x-2=0 (3)/(3)x^2+(5)/(3)x=(2)/(3) x^2+(5)/(3)x=(2)/(3) What value should Marina add to both sides of the equation to complete the square? A ((5)/(6))^2 B ((5)/(3))^2 -(2)/(3) D (10)/(3)

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9 Marina starts to solve the quadratic equation 3x^2+5x-2=0 3x^2+5x-2=0 (3)/(3)x^2+(5)/(3)x=(2)/(3) x^2+(5)/(3)x=(2)/(3) What value should Marina add to both sides of the equation to complete the square? A ((5)/(6))^2 B ((5)/(3))^2 -(2)/(3) D (10)/(3)

9 Marina starts to solve the quadratic equation 3x^2+5x-2=0 3x^2+5x-2=0 (3)/(3)x^2+(5)/(3)x=(2)/(3) x^2+(5)/(3)x=(2)/(3) What value should Marina add to both sides of the equation to complete the square? A ((5)/(6))^2 B ((5)/(3))^2 -(2)/(3) D (10)/(3)

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AntheaMaster · Tutor for 5 years

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To complete the square for an equation in the form of \(x^2 + bx\), you need to add \(\left(\frac{b}{2}\right)^2\) to both sides of the equation.In the given equation \(x^2 + \frac{5}{3}x = \frac{2}{3}\), the value of \(b\) is \(\frac{5}{3}\).So, the value to add to both sides to complete the square is \(\left(\frac{5/3}{2}\right)^2\).\(\left(\frac{5/3}{2}\right)^2 = \left(\frac{5}{6}\right)^2 = \frac{25}{36}\).The correct answer is:(A) \(\left(\frac{5}{6}\right)^2\)
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