Solve x^2-45x^27=-37x^47

Question

Solve the equation

x_{1} = - \frac{81326}{259}, x_{2} = 0, x_{3} = \frac{81326}{259}

Alternative Form

x_{1} \approx - 1.10107, x_{2} = 0, x_{3} \approx 1.10107

Evaluate

x^{2} - 45 x^{2} \times 7 = - 37 x^{4} \times 7

Simplify

More Steps

Evaluate

x^{2} - 45 x^{2} \times 7

Multiply the terms

x^{2} - 315 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 315) x^{2}

Subtract the numbers

- 314 x^{2}

- 314 x^{2} = - 37 x^{4} \times 7

Multiply the terms

- 314 x^{2} = - 259 x^{4}

Add or subtract both sides

- 314 x^{2} - (- 259 x^{4}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 314 x^{2} + 259 x^{4} = 0

Factor the expression

x^{2} (- 314 + 259 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 - 314 + 259 x^{2} = 0

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

x = 0 - 314 + 259 x^{2} = 0

Solve the equation

More Steps

Evaluate

- 314 + 259 x^{2} = 0

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

259 x^{2} = 0 + 314

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

259 x^{2} = 314

Divide both sides

\frac{259 x ^{2}}{259} = \frac{314}{259}

Divide the numbers

x^{2} = \frac{314}{259}

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

x = \pm \frac{314}{259}

Simplify the expression

More Steps

Evaluate

\frac{314}{259}

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

\frac{314}{259}

Multiply by the Conjugate

\frac{314 \times 259}{259 \times 259}

Multiply the numbers

\frac{81326}{259 \times 259}

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

\frac{81326}{259}

x = \pm \frac{81326}{259}

Separate the equation into 2 possible cases

x = \frac{81326}{259} x = - \frac{81326}{259}

x = 0 x = \frac{81326}{259} x = - \frac{81326}{259}

Solution

x_{1} = - \frac{81326}{259}, x_{2} = 0, x_{3} = \frac{81326}{259}

Alternative Form

x_{1} \approx - 1.10107, x_{2} = 0, x_{3} \approx 1.10107

Show Solution

Solve the equation

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