49t^2 + 42t + 9
t=-3/7 or -0.428
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The given expression is a quadratic polynomial in the form ax^2 + bx + c, where a = 49, b = 42, and c = 9.
To simplify this expression, you can use different methods depending on what you want to achieve. If you want to factorize the expression, you can start by determining the factors of the coefficient a and c, and then use the factoring method accordingly. However, in this case, the expression does not factorize easily.
An alternative method is to use the quadratic formula to find the roots (solutions) of the expression. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the roots can be calculated using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
By substituting the values from the given expression into the quadratic formula, you can calculate the roots of the expression. In this case, a = 49, b = 42, and c = 9.
x = (-42 ± √(42^2 - 4 * 49 * 9)) / (2 * 49)
After simplification, you get:
x = (-42 ± √(1764 - 1764)) / 98
Since the discriminant (b^2 - 4ac) is zero, there is only one root for this expression. The expression simplifies to:
x = -42 / 98
Further simplification gives:
x = -21 / 49
So, the simplified expression is -21 / 49.