Solve a1000a-7 - ScanMath

Question

Simplify the expression

1000 a^{2} - 7

Evaluate

a \times 1000 a - 7

Solution

More Steps

Evaluate

a \times 1000 a

Multiply the terms

a^{2} \times 1000

Use the commutative property to reorder the terms

1000 a^{2}

1000 a^{2} - 7

Show Solution

a_{1} = - \frac{70}{100}, a_{2} = \frac{70}{100}

Alternative Form

a_{1} \approx - 0.083666, a_{2} \approx 0.083666

Evaluate

a \times 1000 a - 7

To find the roots of the expression,set the expression equal to 0

a \times 1000 a - 7 = 0

Multiply

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Multiply the terms

a \times 1000 a

Multiply the terms

a^{2} \times 1000

Use the commutative property to reorder the terms

1000 a^{2}

1000 a^{2} - 7 = 0

Move the constant to the right-hand side and change its sign

1000 a^{2} = 0 + 7

Removing 0 doesn't change the value,so remove it from the expression

1000 a^{2} = 7

Divide both sides

\frac{1000 a ^{2}}{1000} = \frac{7}{1000}

Divide the numbers

a^{2} = \frac{7}{1000}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm \frac{7}{1000}

Simplify the expression

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Evaluate

\frac{7}{1000}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{7}{1000}

Simplify the radical expression

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Evaluate

1000

Write the expression as a product where the root of one of the factors can be evaluated

100 \times 10

Write the number in exponential form with the base of 10

1 0^{2} \times 10

The root of a product is equal to the product of the roots of each factor

1 0^{2} \times 10

Reduce the index of the radical and exponent with 2

1010

\frac{7}{10 10}

Multiply by the Conjugate

\frac{7 \times 10}{10 10 \times 10}

Multiply the numbers

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Evaluate

7 \times 10

The product of roots with the same index is equal to the root of the product

7 \times 10

Calculate the product

70

\frac{70}{10 10 \times 10}

Multiply the numbers

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Evaluate

1010 \times 10

When a square root of an expression is multiplied by itself,the result is that expression

10 \times 10

Multiply the numbers

100

\frac{70}{100}

a = \pm \frac{70}{100}

Separate the equation into 2 possible cases

a = \frac{70}{100} a = - \frac{70}{100}

Solution

a_{1} = - \frac{70}{100}, a_{2} = \frac{70}{100}

Alternative Form

a_{1} \approx - 0.083666, a_{2} \approx 0.083666

Show Solution