Solve x 102x-5*10

Question

Simplify the expression

102 x^{2} - 50

Evaluate

x \times 102 x - 5 \times 10

Multiply

More Steps

Multiply the terms

x \times 102 x

Multiply the terms

x^{2} \times 102

Use the commutative property to reorder the terms

102 x^{2}

102 x^{2} - 5 \times 10

Solution

102 x^{2} - 50

Show Solution

2 (51 x^{2} - 25)

Evaluate

x \times 102 x - 5 \times 10

Multiply

More Steps

Multiply the terms

x \times 102 x

Multiply the terms

x^{2} \times 102

Use the commutative property to reorder the terms

102 x^{2}

102 x^{2} - 5 \times 10

Multiply the numbers

102 x^{2} - 50

Solution

2 (51 x^{2} - 25)

Show Solution

x_{1} = - \frac{5 51}{51}, x_{2} = \frac{5 51}{51}

Alternative Form

x_{1} \approx - 0.70014, x_{2} \approx 0.70014

Evaluate

x \times 102 x - 5 \times 10

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

x \times 102 x - 5 \times 10 = 0

Multiply

More Steps

Multiply the terms

x \times 102 x

Multiply the terms

x^{2} \times 102

Use the commutative property to reorder the terms

102 x^{2}

102 x^{2} - 5 \times 10 = 0

Multiply the numbers

102 x^{2} - 50 = 0

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

102 x^{2} = 0 + 50

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

102 x^{2} = 50

Divide both sides

\frac{102 x ^{2}}{102} = \frac{50}{102}

Divide the numbers

x^{2} = \frac{50}{102}

Cancel out the common factor 2

x^{2} = \frac{25}{51}

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

x = \pm \frac{25}{51}

Simplify the expression

More Steps

Evaluate

\frac{25}{51}

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

\frac{25}{51}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{51}

Multiply by the Conjugate

\frac{5 51}{51 \times 51}

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

\frac{5 51}{51}

x = \pm \frac{5 51}{51}

Separate the equation into 2 possible cases

x = \frac{5 51}{51} x = - \frac{5 51}{51}

Solution

x_{1} = - \frac{5 51}{51}, x_{2} = \frac{5 51}{51}

Alternative Form

x_{1} \approx - 0.70014, x_{2} \approx 0.70014

Show Solution