Question 675635
f(x) = {{{(1/2)x^2 + (3/2)x - (1/2)}}}
{{{0 = (1/2)x^2 + (3/2)x - (1/2)}}}
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Multiply both sides of the equation by 2
{{{0 = x^2 + 3x - 1}}}
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Complete the square
{{{x^2 + 3x + 2.25 = 1 + 2.25}}}
{{{(x+1.5)^2 = 3.25}}}
{{{sqrt(x+1.5)^2}}} = +/- {{{sqrt(3.25)}}}
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x+1.5 = +/- {{{sqrt(3.25)}}}
x = -1.5 +/- {{{sqrt(3.25)}}}
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x = -1.5 + 1.8 = {{{highlight_green(.3)}}}
x = -1.5 - 1.8 = {{{highlight_green(-3.3)}}}
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using the quadratic formula
x = {{{(-(3/2) +- sqrt((3/2)^2-4(1/2)(-1/2)))/2(1/2)}}}
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x = {{{(-(3/2) +- sqrt((9/4)-(-2/2)))/(2/2)}}}
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x = {{{(-3/2) +- sqrt((9/4)+1))/1}}}
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x = {{{(-3/2) +- sqrt((9/4)+1(4/4))}}}
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x = {{{(-3/2) +- sqrt(13/4)}}}
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x = {{{(-3/2) +- (sqrt(13)/2)}}}
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x = {{{((-3)+- sqrt(13))/2}}}
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