Question 1005383
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{{{y=4x^2-6x-10}}}
{{{y=25-2x}}}
Since both equal y:
{{{4x^2-6x-10=25-2x}}}
{{{4x^2-4x-35=0}}}
{{{(4x+10)(x-3.5)=0}}}
{{{4x+10=0}}} {{{OR}}} {{{x-3.5=0}}}
{{{4x=-10}}} {{{OR}}} {{{x=3.5}}}
{{{x=-2.5}}} {{{OR}}} {{{x=3.5}}}
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Using x=(-2.5):
{{{y=25-2x}}}
{{{y=25-2(-2.5)}}}
{{{y=25-(-5)}}}
{{{y=30}}}
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CHECK (Using other equation):
{{{y=4x^2-6x-10}}}
{{{30=4(-2.5)^2-6(-2.5)-10}}}
{{{30=4(6.25)-(-15)-10}}}
{{{30=25+15-10}}}
{{{30=40-10}}}
{{{30=30}}}
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Using x=3.5:
{{{y=25-2x}}}
{{{y=25-2(3.5)}}}
{{{y=25-7}}}
{{{y=18}}}
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CHECK:
{{{y=4x^2-6x-10}}}
{{{18=4(3.5)^2-6(3.5)-10}}}
{{{18=4(12.25)-21-10}}}
{{{18=49-31}}}
{{{18=18}}}
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ANSWER: The solutions are (-2.5,30) and (3.5,18)