Equations with One Variable

$\blacktriangleright$ To solve an equation with one variable

1.
Place the insertion point in the equation.

2.
From the Solve submenu, choose Exact.

Scientific Notebook returns a solution. Note that in the following examples, integer or rational coefficients yield algebraic solutions and real (floating-point) coefficients yield decimal approximations. All solutions are found for polynomial equations, including complex solutions.

$\blacktriangleright$ Solve + Exact

5x2 + 3x = 1, Solution is : $\left\{\vphantom{ x=-% \dfrac{3}{10}+\dfrac{1}{10}\sqrt{29}}\right.$x = - ${\dfrac{{3}}{{10}}}$ + ${\dfrac{{1}}{{10}}}$$\sqrt{{29}}$$\left.\vphantom{ x=-% \dfrac{3}{10}+\dfrac{1}{10}\sqrt{29}}\right\}$, $\left\{\vphantom{ x=-\dfrac{3}{10}-% \dfrac{1}{10}\sqrt{29}}\right.$x = - ${\dfrac{{3}}{{10}}}$ - ${\dfrac{{1}}{{10}}}$$\sqrt{{29}}$$\left.\vphantom{ x=-\dfrac{3}{10}-% \dfrac{1}{10}\sqrt{29}}\right\}$

5x2 + 3x = 1.0, Solution is : $\left\{\vphantom{ x=.239}\right.$x = .239$\left.\vphantom{ x=.239}\right\}$, $\left\{\vphantom{ x=-.839}\right.$x = - .839$\left.\vphantom{ x=-.839}\right\}$

s2 +10s + ${\dfrac{{1681}}{{64}}}$ = 0, Solution is : $\left\{\vphantom{ s=-5+\dfrac{9}{8}% i}\right.$s = - 5 + ${\dfrac{{9}}{{8}% }}$i$\left.\vphantom{ s=-5+\dfrac{9}{8}% i}\right\}$, $\left\{\vphantom{ s=-5-\dfrac{9}{8}i}\right.$s = - 5 - ${\dfrac{{9}}{{8}}}$i$\left.\vphantom{ s=-5-\dfrac{9}{8}i}\right\}$

s2 + $\left(\vphantom{ 10.0}\right.$10.0$\left.\vphantom{ 10.0}\right)$s + ${\dfrac{{1681}}{{64}}}$ = 0, Solution is : $\left\{\vphantom{ s=-5.0+1.125i}\right.$s = - 5.0 + 1.125i$\left.\vphantom{ s=-5.0+1.125i}\right\}$, $\left\{\vphantom{ s=-5.0-1.125i}\right.$s = - 5.0 - 1.125i$\left.\vphantom{ s=-5.0-1.125i}\right\}$

Scientific Notebook displays multiple roots in some cases.

$\blacktriangleright$ Solve + Exact

$\left(\vphantom{ x-5}\right.$x - 5$\left.\vphantom{ x-5}\right)^{{3}}_{}$ = 0, Solution is : $\left\{\vphantom{ x=5}\right.$x = 5$\left.\vphantom{ x=5}\right\}$, $\left\{\vphantom{ x=5}\right.$x = 5$\left.\vphantom{ x=5}\right\}$, $\left\{\vphantom{ x=5}\right.$x = 5$\left.\vphantom{ x=5}\right\}$

You can solve equations with rational expressions.

$\blacktriangleright$ Solve + Exact

${\dfrac{{14}}{{a+2}}}$ - ${\dfrac{{1}}{{a-4}}}$ = 1, Solution is : $\left\{\vphantom{ a=5}\right.$a = 5$\left.\vphantom{ a=5}\right\}$, $\left\{\vphantom{ a=10}\right.$a = 10$\left.\vphantom{ a=10}\right\}$

You can solve equations involving absolute values.

$\blacktriangleright$ Solve + Exact

$\left\vert\vphantom{ 3x-2}\right.$3x - 2$\left.\vphantom{ 3x-2}\right\vert$ = 5, Solution is : $\left\{\vphantom{ x=\dfrac{7}{3}}\right.$x = ${\dfrac{{7}}{{3}}}$$\left.\vphantom{ x=\dfrac{7}{3}}\right\}$, $\left\{\vphantom{ x=-1}\right.$x = - 1$\left.\vphantom{ x=-1}\right\}$


Subsections