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Sagot :
Given
[tex]x^2+10x-2=0[/tex]You have to determine both possible values of x by using the quadratic formula, which is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient that multiplies the quadratic term of the quadratic expression
b is the coefficient of the x term
c is the constant
For the given expression, the values of the coefficients are:
a=1
b=10
c=-2
Replace said coefficients in the formula and solve
[tex]\begin{gathered} x=\frac{-10\pm\sqrt[]{10^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ x=\frac{-10\pm\sqrt[]{100+8}}{2} \\ x=\frac{-10\pm\sqrt[]{108}}{2} \end{gathered}[/tex]Now you have to solve the addition and subtraction separately
Addition
[tex]\begin{gathered} x=\frac{-10+\sqrt[]{108}}{2} \\ x=0.196 \\ x\approx0.2 \end{gathered}[/tex]Subtraction
[tex]\begin{gathered} x=\frac{-10-\sqrt[]{108}}{2} \\ x=-10.196 \\ x\approx-10.20 \end{gathered}[/tex]The possible values of x are -10.20 and 0.20.
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