Solve 45x^2-2 - ScanMath

Question

Find the roots

x_{1} = - \frac{10}{15}, x_{2} = \frac{10}{15}

Alternative Form

x_{1} \approx - 0.210819, x_{2} \approx 0.210819

Evaluate

45 x^{2} - 2

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

45 x^{2} - 2 = 0

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

45 x^{2} = 0 + 2

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

45 x^{2} = 2

Divide both sides

\frac{45 x ^{2}}{45} = \frac{2}{45}

Divide the numbers

x^{2} = \frac{2}{45}

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

x = \pm \frac{2}{45}

Simplify the expression

More Steps

Evaluate

\frac{2}{45}

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

\frac{2}{45}

Simplify the radical expression

More Steps

Evaluate

45

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

9 \times 5

Write the number in exponential form with the base of 3

3^{2} \times 5

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

3^{2} \times 5

Reduce the index of the radical and exponent with 2

35

\frac{2}{3 5}

Multiply by the Conjugate

\frac{2 \times 5}{3 5 \times 5}

Multiply the numbers

More Steps

Evaluate

2 \times 5

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

2 \times 5

Calculate the product

10

\frac{10}{3 5 \times 5}

Multiply the numbers

More Steps

Evaluate

35 \times 5

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

3 \times 5

Multiply the terms

15

\frac{10}{15}

x = \pm \frac{10}{15}

Separate the equation into 2 possible cases

x = \frac{10}{15} x = - \frac{10}{15}

Solution

x_{1} = - \frac{10}{15}, x_{2} = \frac{10}{15}

Alternative Form

x_{1} \approx - 0.210819, x_{2} \approx 0.210819

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