Answer:
[tex]\mathrm{x_1=99/49-\sqrt38221/49;x_2=99/49+\sqrt38221/49}\\[/tex]
Step-by-step explanation:
Analyze the function:
f(x)=[tex]-4.9x^{2}[/tex]+19.8x+58
To find the x-intercept, set y=0:
[tex]-4.9x^{2}[/tex] + [tex]19.8_{x}[/tex] + 58 = 0
Convert decimal to fraction:
[tex]-\frac{49}{10}x^{2}[/tex] + [tex]\frac{99}{5}[/tex]x+58=0
Reduce the fraction:
[tex]-\frac{49}{10}[/tex] [tex]x^{2}[/tex] + [tex]\frac{99}{5}[/tex] x + 58 = 0
Multiply both sides of the equation by the common denominator:
[tex]-\frac{49x10}{10}[/tex]×[tex]x^{2}[/tex]+[tex]\frac{99x10}{5} x[/tex] × + 58 × 10 = 0 × 10
Reduce the fractions:
[tex]-49x^{2}+198x[/tex] + 58 × 10 = 0 × 10
Calculate the product or quotient:
-49[tex]x^{2}+198x+580=0[/tex]
Make the leading coefficient positive:
49[tex]x^{2} -198x-580=0[/tex]
Identify the coefficients:
a = 49, b = -198, c = -580
Substitute into x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-198\right)+\sqrt{{(-198)}^2-4\times49\times(-580)}}{2\times49}\\[/tex]
or
[tex]x=\frac{-(-198)-\sqrt{{(-198)}^2-4\times49\times(-580)}}{2\times49}[/tex]
Combine the results:
[tex]x=\frac{99+\sqrt{38221}}{49}\ or\ x=\frac{99\ -\ \sqrt{38221}}{49}\\\\[/tex]
