Solve 47-343x^2 - ScanMath

Question

Find the roots

x_{1} = - \frac{329}{49}, x_{2} = \frac{329}{49}

Alternative Form

x_{1} \approx - 0.370171, x_{2} \approx 0.370171

Evaluate

47 - 343 x^{2}

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

47 - 343 x^{2} = 0

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

- 343 x^{2} = 0 - 47

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

- 343 x^{2} = - 47

Change the signs on both sides of the equation

343 x^{2} = 47

Divide both sides

\frac{343 x ^{2}}{343} = \frac{47}{343}

Divide the numbers

x^{2} = \frac{47}{343}

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

x = \pm \frac{47}{343}

Simplify the expression

More Steps

Evaluate

\frac{47}{343}

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

\frac{47}{343}

Simplify the radical expression

More Steps

Evaluate

343

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

49 \times 7

Write the number in exponential form with the base of 7

7^{2} \times 7

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

7^{2} \times 7

Reduce the index of the radical and exponent with 2

77

\frac{47}{7 7}

Multiply by the Conjugate

\frac{47 \times 7}{7 7 \times 7}

Multiply the numbers

More Steps

Evaluate

47 \times 7

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

47 \times 7

Calculate the product

329

\frac{329}{7 7 \times 7}

Multiply the numbers

More Steps

Evaluate

77 \times 7

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

7 \times 7

Multiply the numbers

49

\frac{329}{49}

x = \pm \frac{329}{49}

Separate the equation into 2 possible cases

x = \frac{329}{49} x = - \frac{329}{49}

Solution

x_{1} = - \frac{329}{49}, x_{2} = \frac{329}{49}

Alternative Form

x_{1} \approx - 0.370171, x_{2} \approx 0.370171

Show Solution