Solve for t
t = \frac{50}{7} = 7\frac{1}{7} \approx 7.142857143
t=0
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t\left(10-1.4t\right)=0
Factor out t.
t=0 t=\frac{50}{7}
To find equation solutions, solve t=0 and 10-\frac{7t}{5}=0.
-1.4t^{2}+10t=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
t=\frac{-10±\sqrt{10^{2}}}{2\left(-1.4\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1.4 for a, 10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
t=\frac{-10±10}{2\left(-1.4\right)}
Take the square root of 10^{2}.
t=\frac{-10±10}{-2.8}
Multiply 2 times -1.4.
t=\frac{0}{-2.8}
Now solve the equation t=\frac{-10±10}{-2.8} when ± is plus. Add -10 to 10.
t=0
Divide 0 by -2.8 by multiplying 0 by the reciprocal of -2.8.
t=-\frac{20}{-2.8}
Now solve the equation t=\frac{-10±10}{-2.8} when ± is minus. Subtract 10 from -10.
t=\frac{50}{7}
Divide -20 by -2.8 by multiplying -20 by the reciprocal of -2.8.
t=0 t=\frac{50}{7}
The equation is now solved.
-1.4t^{2}+10t=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{-1.4t^{2}+10t}{-1.4}=\frac{0}{-1.4}
Divide both sides of the equation by -1.4, which is the same as multiplying both sides by the reciprocal of the fraction.
t^{2}+\frac{10}{-1.4}t=\frac{0}{-1.4}
Dividing by -1.4 undoes the multiplication by -1.4.
t^{2}-\frac{50}{7}t=\frac{0}{-1.4}
Divide 10 by -1.4 by multiplying 10 by the reciprocal of -1.4.
t^{2}-\frac{50}{7}t=0
Divide 0 by -1.4 by multiplying 0 by the reciprocal of -1.4.
t^{2}-\frac{50}{7}t+\left(-\frac{25}{7}\right)^{2}=\left(-\frac{25}{7}\right)^{2}
Divide -\frac{50}{7}, the coefficient of the x term, by 2 to get -\frac{25}{7}. Then add the square of -\frac{25}{7} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
t^{2}-\frac{50}{7}t+\frac{625}{49}=\frac{625}{49}
Square -\frac{25}{7} by squaring both the numerator and the denominator of the fraction.
\left(t-\frac{25}{7}\right)^{2}=\frac{625}{49}
Factor t^{2}-\frac{50}{7}t+\frac{625}{49}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(t-\frac{25}{7}\right)^{2}}=\sqrt{\frac{625}{49}}
Take the square root of both sides of the equation.
t-\frac{25}{7}=\frac{25}{7} t-\frac{25}{7}=-\frac{25}{7}
Simplify.
t=\frac{50}{7} t=0
Add \frac{25}{7} to both sides of the equation.
Examples
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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