Question 964131
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{{{2x=sqrt(4x^2-8x-9)}}} Square both sides
{{{4x^2=4x^2-8x-9}}} Subtract {{{4x^2}}} from each side.
{{{0=-8x-9}}} Add 8x to each side.
{{{8x=-9}}} Divide each side by 8
{{{x=-9/8}}}
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CHECK:
{{{2(-9/8)=sqrt(4(-9/8)^2-8(-9/8)-9)}}}
{{{-18/8=sqrt(4(81/64)+9-9)}}}
{{{-18/8=sqrt(324/64)}}}
{{{-18/8}}}=+-{{{(18/8)}}}
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{{{3x=sqrt(8x^2+9)}}} Square both sides.
{{{9x^2=8x^2+9}}} Subtract {{{8x^2}}} from each side.
{{{x^2=9}}} Find the square root of each side.
{{{x=3}}}
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CHECK:
{{{3x=sqrt(8x^2+9)}}}
{{{3(3)=sqrt(8(3^2)+9)}}}
{{{9=sqrt(72+9)}}}
{{{9=sqrt(81)}}}
{{{9}}}=+-{{{9}}}
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{{{sqrt(-5x)=sqrt(x+4)}}} Square both sides.
{{{-5x=x+4}}} Subtract x from each side.
{{{-6x=4}}} Divide each side by -6.
{{{x=-4/6}}}={{{-2/3}}}
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CHECK:
{{{sqrt(-5x)=sqrt(x+4)}}}
{{{sqrt(-5(-2/3))=sqrt((-2/3)+4)}}}
{{{sqrt(10/3)=sqrt((-2/3)+12/3)}}}
{{{sqrt(10/3)=sqrt(10/3)}}}