Solve for m
m = \frac{33}{4} = 8\frac{1}{4} = 8.25
m=0
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m\left(4m-33\right)=0
Factor out m.
m=0 m=\frac{33}{4}
To find equation solutions, solve m=0 and 4m-33=0.
4m^{2}-33m=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.
m=\frac{-\left(-33\right)±\sqrt{\left(-33\right)^{2}}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -33 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
m=\frac{-\left(-33\right)±33}{2\times 4}
Take the square root of \left(-33\right)^{2}.
m=\frac{33±33}{2\times 4}
The opposite of -33 is 33.
m=\frac{33±33}{8}
Multiply 2 times 4.
m=\frac{66}{8}
Now solve the equation m=\frac{33±33}{8} when ± is plus. Add 33 to 33.
m=\frac{33}{4}
Reduce the fraction \frac{66}{8} to lowest terms by extracting and canceling out 2.
m=\frac{0}{8}
Now solve the equation m=\frac{33±33}{8} when ± is minus. Subtract 33 from 33.
m=0
Divide 0 by 8.
m=\frac{33}{4} m=0
The equation is now solved.
4m^{2}-33m=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{4m^{2}-33m}{4}=\frac{0}{4}
Divide both sides by 4.
m^{2}-\frac{33}{4}m=\frac{0}{4}
Dividing by 4 undoes the multiplication by 4.
m^{2}-\frac{33}{4}m=0
Divide 0 by 4.
m^{2}-\frac{33}{4}m+\left(-\frac{33}{8}\right)^{2}=\left(-\frac{33}{8}\right)^{2}
Divide -\frac{33}{4}, the coefficient of the x term, by 2 to get -\frac{33}{8}. Then add the square of -\frac{33}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
m^{2}-\frac{33}{4}m+\frac{1089}{64}=\frac{1089}{64}
Square -\frac{33}{8} by squaring both the numerator and the denominator of the fraction.
\left(m-\frac{33}{8}\right)^{2}=\frac{1089}{64}
Factor m^{2}-\frac{33}{4}m+\frac{1089}{64}. 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(m-\frac{33}{8}\right)^{2}}=\sqrt{\frac{1089}{64}}
Take the square root of both sides of the equation.
m-\frac{33}{8}=\frac{33}{8} m-\frac{33}{8}=-\frac{33}{8}
Simplify.
m=\frac{33}{4} m=0
Add \frac{33}{8} to both sides of the equation.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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