Solve for x
x = \frac{\sqrt{193} + 1}{8} \approx 1.861555499
x=\frac{1-\sqrt{193}}{8}\approx -1.611555499
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4x^{2}+x\times 2=3\left(x+4\right)
Use the distributive property to multiply x\times 2 by 2x+1.
4x^{2}+x\times 2=3x+12
Use the distributive property to multiply 3 by x+4.
4x^{2}+x\times 2-3x=12
Subtract 3x from both sides.
4x^{2}-x=12
Combine x\times 2 and -3x to get -x.
4x^{2}-x-12=0
Subtract 12 from both sides.
x=\frac{-\left(-1\right)±\sqrt{1-4\times 4\left(-12\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -1 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-1\right)±\sqrt{1-16\left(-12\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{-\left(-1\right)±\sqrt{1+192}}{2\times 4}
Multiply -16 times -12.
x=\frac{-\left(-1\right)±\sqrt{193}}{2\times 4}
Add 1 to 192.
x=\frac{1±\sqrt{193}}{2\times 4}
The opposite of -1 is 1.
x=\frac{1±\sqrt{193}}{8}
Multiply 2 times 4.
x=\frac{\sqrt{193}+1}{8}
Now solve the equation x=\frac{1±\sqrt{193}}{8} when ± is plus. Add 1 to \sqrt{193}.
x=\frac{1-\sqrt{193}}{8}
Now solve the equation x=\frac{1±\sqrt{193}}{8} when ± is minus. Subtract \sqrt{193} from 1.
x=\frac{\sqrt{193}+1}{8} x=\frac{1-\sqrt{193}}{8}
The equation is now solved.
4x^{2}+x\times 2=3\left(x+4\right)
Use the distributive property to multiply x\times 2 by 2x+1.
4x^{2}+x\times 2=3x+12
Use the distributive property to multiply 3 by x+4.
4x^{2}+x\times 2-3x=12
Subtract 3x from both sides.
4x^{2}-x=12
Combine x\times 2 and -3x to get -x.
\frac{4x^{2}-x}{4}=\frac{12}{4}
Divide both sides by 4.
x^{2}-\frac{1}{4}x=\frac{12}{4}
Dividing by 4 undoes the multiplication by 4.
x^{2}-\frac{1}{4}x=3
Divide 12 by 4.
x^{2}-\frac{1}{4}x+\left(-\frac{1}{8}\right)^{2}=3+\left(-\frac{1}{8}\right)^{2}
Divide -\frac{1}{4}, the coefficient of the x term, by 2 to get -\frac{1}{8}. Then add the square of -\frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{1}{4}x+\frac{1}{64}=3+\frac{1}{64}
Square -\frac{1}{8} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{1}{4}x+\frac{1}{64}=\frac{193}{64}
Add 3 to \frac{1}{64}.
\left(x-\frac{1}{8}\right)^{2}=\frac{193}{64}
Factor x^{2}-\frac{1}{4}x+\frac{1}{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(x-\frac{1}{8}\right)^{2}}=\sqrt{\frac{193}{64}}
Take the square root of both sides of the equation.
x-\frac{1}{8}=\frac{\sqrt{193}}{8} x-\frac{1}{8}=-\frac{\sqrt{193}}{8}
Simplify.
x=\frac{\sqrt{193}+1}{8} x=\frac{1-\sqrt{193}}{8}
Add \frac{1}{8} to both sides of the equation.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}