Solve 9a 106a-1 - ScanMath

Question

Simplify the expression

954 a^{2} - 1

Evaluate

9 a \times 106 a - 1

Solution

More Steps

Evaluate

9 a \times 106 a

Multiply the terms

954 a \times a

Multiply the terms

954 a^{2}

954 a^{2} - 1

Show Solution

a_{1} = - \frac{106}{318}, a_{2} = \frac{106}{318}

Alternative Form

a_{1} \approx - 0.032376, a_{2} \approx 0.032376

Evaluate

9 a \times 106 a - 1

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

9 a \times 106 a - 1 = 0

Multiply

More Steps

Multiply the terms

9 a \times 106 a

Multiply the terms

954 a \times a

Multiply the terms

954 a^{2}

954 a^{2} - 1 = 0

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

954 a^{2} = 0 + 1

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

954 a^{2} = 1

Divide both sides

\frac{954 a ^{2}}{954} = \frac{1}{954}

Divide the numbers

a^{2} = \frac{1}{954}

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

a = \pm \frac{1}{954}

Simplify the expression

More Steps

Evaluate

\frac{1}{954}

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

\frac{1}{954}

Simplify the radical expression

\frac{1}{954}

Simplify the radical expression

More Steps

Evaluate

954

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

9 \times 106

Write the number in exponential form with the base of 3

3^{2} \times 106

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

3^{2} \times 106

Reduce the index of the radical and exponent with 2

3106

\frac{1}{3 106}

Multiply by the Conjugate

\frac{106}{3 106 \times 106}

Multiply the numbers

More Steps

Evaluate

3106 \times 106

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

3 \times 106

Multiply the terms

318

\frac{106}{318}

a = \pm \frac{106}{318}

Separate the equation into 2 possible cases

a = \frac{106}{318} a = - \frac{106}{318}

Solution

a_{1} = - \frac{106}{318}, a_{2} = \frac{106}{318}

Alternative Form

a_{1} \approx - 0.032376, a_{2} \approx 0.032376

Show Solution