# Evaluate: 3x^2-10=-5

## Expression: $3{x}^{2}-10=-5$

Move the constant to the left-hand side and change its sign

$3{x}^{2}-10+5=0$

Calculate the sum

$3{x}^{2}-5=0$

Write the quadratic equation in the appropriate form

${x}^{2}-\frac{ 5 }{ 3 }=0$

Identify the coefficients $p$ and $q$ of the quadratic equation

$\begin{array} { l }p=0,& q=-\frac{ 5 }{ 3 }\end{array}$

Substitute $p=0$ and $q=-\frac{ 5 }{ 3 }$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$

$x=-\frac{ 0 }{ 2 }\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -\frac{ 5 }{ 3 } \right) }$

$0$ divided by any non-zero expression equals $0$

$x=-0\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -\frac{ 5 }{ 3 } \right) }$

$0$ divided by any non-zero expression equals $0$

$x=-0\pm\sqrt{ {0}^{2}-\left( -\frac{ 5 }{ 3 } \right) }$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$x=-0\pm\sqrt{ {0}^{2}+\frac{ 5 }{ 3 } }$

Removing $0$ doesn't change the value, so remove it from the expression

$x=\sqrt{ {0}^{2}+\frac{ 5 }{ 3 } }$

$0$ raised to any positive power equals $0$

$x=\sqrt{ 0+\frac{ 5 }{ 3 } }$

Removing $0$ doesn't change the value, so remove it from the expression

$x=\sqrt{ \frac{ 5 }{ 3 } }$

To take a root of a fraction, take the root of the numerator and denominator separately

$x=\frac{ \sqrt{ 5 } }{ \sqrt{ 3 } }$

Rationalize the denominator

$x=\frac{ \sqrt{ 15 } }{ 3 }$

Write the solutions, one with a $+$ sign and one with a $-$ sign

$\begin{array} { l }x=\frac{ \sqrt{ 15 } }{ 3 },\\x=-\frac{ \sqrt{ 15 } }{ 3 }\end{array}$

The equation has $2$ solutions

\begin{align*}&\begin{array} { l }x_1=-\frac{ \sqrt{ 15 } }{ 3 },& x_2=\frac{ \sqrt{ 15 } }{ 3 }\end{array} \\&\begin{array} { l }x_1\approx-1.29099,& x_2\approx1.29099\end{array}\end{align*}

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