Solve s a= 1000 a^2=s - Socratic AI (ScanMath)

Evaluate

{s a = 1000 a^{2} 1000 a^{2} = s

Rewrite the expression

{s a = 1000 a^{2} s = 1000 a^{2}

Substitute the given value of s into the equation s a = 1000 a^{2}

1000 a^{2} \times a = 1000 a^{2}

Multiply the terms

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1000 a^{3} = 1000 a^{2}

Add or subtract both sides

1000 a^{3} - 1000 a^{2} = 0

Factor the expression

1000 a^{2} (a - 1) = 0

Divide both sides

a^{2} (a - 1) = 0

Separate the equation into 2 possible cases

a^{2} = 0 \cup a - 1 = 0

The only way a power can be 0 is when the base equals 0

a = 0 \cup a - 1 = 0

Solve the equation

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a = 0 \cup a = 1

Rearrange the terms

{a = 0 s = 1000 a^{2} \cup {a = 1 s = 1000 a^{2}

Calculate

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{a = 0 s = 0 \cup {a = 1 s = 1000 a^{2}

Calculate

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{a = 0 s = 0 \cup {a = 1 s = 1000

Check the solution

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{a = 0 s = 0 \cup {a = 1 s = 1000

Check the solution

More Steps

{a = 0 s = 0 \cup {a = 1 s = 1000

Solution

(a_{1}, s_{1}) = (0, 0) (a_{2}, s_{2}) = (1, 1000)

S a= 1000 a^2=s