# Solve Using the Square Root Property 0=0.014x^2-1.18x+24.23 0=0.014×2-1.18x+24.23
Rewrite the equation as 0.014×2-1.18x+24.23=0.
0.014×2-1.18x+24.23=0
Factor 0.002 out of 0.014×2-1.18x+24.23.
Factor 0.002 out of 0.014×2.
0.002(7×2)-1.18x+24.23=0
Factor 0.002 out of -1.18x.
0.002(7×2)+0.002(-590x)+24.23=0
Factor 0.002 out of 24.23.
0.002(7×2)+0.002(-590x)+0.002(12115)=0
Factor 0.002 out of 0.002(7×2)+0.002(-590x).
0.002(7×2-590x)+0.002(12115)=0
Factor 0.002 out of 0.002(7×2-590x)+0.002(12115).
0.002(7×2-590x+12115)=0
0.002(7×2-590x+12115)=0
Divide each term by 0.002 and simplify.
Divide each term in 0.002(7×2-590x+12115)=0 by 0.002.
0.002(7×2-590x+12115)0.002=00.002
Cancel the common factor of 0.002.
7×2-590x+12115=00.002
Divide 0 by 0.002.
7×2-590x+12115=0
7×2-590x+12115=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=7, b=-590, and c=12115 into the quadratic formula and solve for x.
590±(-590)2-4⋅(7⋅12115)2⋅7
Simplify.
Simplify the numerator.
Raise -590 to the power of 2.
x=590±348100-4⋅(7⋅12115)2⋅7
Multiply 7 by 12115.
x=590±348100-4⋅848052⋅7
Multiply -4 by 84805.
x=590±348100-3392202⋅7
Subtract 339220 from 348100.
x=590±88802⋅7
Rewrite 8880 as 42⋅555.
Factor 16 out of 8880.
x=590±16(555)2⋅7
Rewrite 16 as 42.
x=590±42⋅5552⋅7
x=590±42⋅5552⋅7
Pull terms out from under the radical.
x=590±45552⋅7
x=590±45552⋅7
Multiply 2 by 7.
x=590±455514
Simplify 590±455514.
x=295±25557
x=295±25557
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -590 to the power of 2.
x=590±348100-4⋅(7⋅12115)2⋅7
Multiply 7 by 12115.
x=590±348100-4⋅848052⋅7
Multiply -4 by 84805.
x=590±348100-3392202⋅7
Subtract 339220 from 348100.
x=590±88802⋅7
Rewrite 8880 as 42⋅555.
Factor 16 out of 8880.
x=590±16(555)2⋅7
Rewrite 16 as 42.
x=590±42⋅5552⋅7
x=590±42⋅5552⋅7
Pull terms out from under the radical.
x=590±45552⋅7
x=590±45552⋅7
Multiply 2 by 7.
x=590±455514
Simplify 590±455514.
x=295±25557
Change the ± to +.
x=295+25557
x=295+25557
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -590 to the power of 2.
x=590±348100-4⋅(7⋅12115)2⋅7
Multiply 7 by 12115.
x=590±348100-4⋅848052⋅7
Multiply -4 by 84805.
x=590±348100-3392202⋅7
Subtract 339220 from 348100.
x=590±88802⋅7
Rewrite 8880 as 42⋅555.
Factor 16 out of 8880.
x=590±16(555)2⋅7
Rewrite 16 as 42.
x=590±42⋅5552⋅7
x=590±42⋅5552⋅7
Pull terms out from under the radical.
x=590±45552⋅7
x=590±45552⋅7
Multiply 2 by 7.
x=590±455514
Simplify 590±455514.
x=295±25557
Change the ± to -.
x=295-25557
x=295-25557
The final answer is the combination of both solutions.
x=295+25557,295-25557
The result can be shown in multiple forms.
Exact Form:
x=295+25557,295-25557
Decimal Form:
x=48.87383942…,35.41187486…
Solve Using the Square Root Property 0=0.014x^2-1.18x+24.23   ## Download our App from the store

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