Question 91593
solve for x using the quadratic formula 3x^2 = 5x + 6
:
Put the equation in the ax^2 + bx + 3 = 0 form
3x^2 - 5x - 6 = 0; subtracted 5x and 6 from both sides
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The quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
In your equation: a = 3; b = -5; c = -6, substitute in the formula:
{{{x = (-(-5) +- sqrt(-5^2 - 4 * 3 * -6 ))/(2*3) }}}
:
{{{x = (+5 +- sqrt(25 - (-72) ))/(6) }}}
:
{{{x = (+5 +- sqrt(25 + 72) )/(6) }}}; minus a minus is a plus
:
{{{x = (+5 +- sqrt(97) )/(6) }}}
:
1st solution:
{{{x = (+5 +9.849 )/(6) }}}; found the square root of 97
{{{x = 14.849/6}}}
x = +2.475
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2nd solution
{{{x = (+5 - 9.849 )/(6) }}}
{{{x = -4.849/6}}}
x = -.808
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Did you understand each step here?
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It's a good idea to substitute at least one of the solutions in the original equation. Try x = 2.475
3x^2 = 5x + 6
3(2.475^2) = 5(2.475) + 6
3(6.126) = 12.375 + 6
18.378 = 18.375; close enough to confirm out solution
:
You can check the -.808 solution the same way
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