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Solve x and express answers in simplist radical forM. 2x^2+3x-=9x+2

Sagot :

Hello

To solve this question, i will use quadratic formula; however, there are other methods we can use to solve this question.

Step 1

Collect like terms

[tex]\begin{gathered} 2x^2+3x=9x+2 \\ 2x^2+3x-9x-2=0 \\ 2x^2-6x-2=0 \end{gathered}[/tex]

A standard quadratic equation can be represented as

[tex]\begin{gathered} ax^2+bx+c=0 \\ a=2,b=-6,c=-2 \end{gathered}[/tex]

The quadratic equation is given as

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

Therefore,

[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(2)(-2)}}{2\times2} \\ x=\frac{6\pm\sqrt[]{36+16}}{4} \\ x=\frac{6\pm\sqrt[]{52}}{4} \\ x=\frac{6\pm7.2}{4} \\ x=\frac{6+7.2}{4}=3.3 \\ or \\ x=\frac{6-7.2}{4}=-0.3 \end{gathered}[/tex]

From the calculations above, the value of x is either 3.3 or -0.3