Solve. Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\sqrt {x-3}}+5=x}
| Foundations
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1) How do you solve for  in the equation Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\sqrt {x}}=5}
?
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| 2) How do you find the zeros of Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f(x)=x^{2}+x-6}
?
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| Answer:
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1) You square both sides of the equation to get  .
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2) You factor  to get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (x+3)(x-2)=0}
. From here, we solve to get  or  .
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Solution:
| Step 1:
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| First, we get the square root by itself. Subtracting 5 from both sides, we get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\sqrt {x-3}}=x-5}
.
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| Step 2:
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| Now, to get rid of the square root, we square both sides of the equation.
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| So, we get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x-3=(x-5)^{2}}
.
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| Step 3:
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| We multiply out the right hand side to get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x-3=x^{2}-10x+25}
.
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| Step 4:
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| Getting all the terms on one side, we have Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 0=x^{2}-11x+28}
.
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| To solve, we can factor to get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 0=(x-7)(x-4)}
.
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| Step 5:
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| The two possible solutions are Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=7}
and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=4}
.
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| But, plugging in Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=4}
into the problem, gives us Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 6={\sqrt {4-3}}+5=4}
, which is not true.
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| Thus, the only solution is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=7}
.
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| Final Answer:
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| Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=7}
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