Solve 42x ⋅ 14x-3

Question

Simplify the expression

588 x^{2} - 3

Evaluate

42 x \times 14 x - 3

Solution

More Steps

Evaluate

42 x \times 14 x

Multiply the terms

588 x \times x

Multiply the terms

588 x^{2}

588 x^{2} - 3

Show Solution

3 (14 x - 1) (14 x + 1)

Evaluate

42 x \times 14 x - 3

Evaluate

More Steps

Evaluate

42 x \times 14 x

Multiply the terms

588 x \times x

Multiply the terms

588 x^{2}

588 x^{2} - 3

Factor out 3 from the expression

3 (196 x^{2} - 1)

Solution

More Steps

Evaluate

196 x^{2} - 1

Rewrite the expression in exponential form

(14 x)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(14 x - 1) (14 x + 1)

3 (14 x - 1) (14 x + 1)

Show Solution

x_{1} = - \frac{1}{14}, x_{2} = \frac{1}{14}

Alternative Form

x_{1} = - 0.0 \dot{7} 1428 \dot{5}, x_{2} = 0.0 \dot{7} 1428 \dot{5}

Evaluate

42 x \times 14 x - 3

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

42 x \times 14 x - 3 = 0

Multiply

More Steps

Multiply the terms

42 x \times 14 x

Multiply the terms

588 x \times x

Multiply the terms

588 x^{2}

588 x^{2} - 3 = 0

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

588 x^{2} = 0 + 3

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

588 x^{2} = 3

Divide both sides

\frac{588 x ^{2}}{588} = \frac{3}{588}

Divide the numbers

x^{2} = \frac{3}{588}

Cancel out the common factor 3

x^{2} = \frac{1}{196}

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

x = \pm \frac{1}{196}

Simplify the expression

More Steps

Evaluate

\frac{1}{196}

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

\frac{1}{196}

Simplify the radical expression

\frac{1}{196}

Simplify the radical expression

More Steps

Evaluate

196

Write the number in exponential form with the base of 14

1 4^{2}

Reduce the index of the radical and exponent with 2

14

\frac{1}{14}

x = \pm \frac{1}{14}

Separate the equation into 2 possible cases

x = \frac{1}{14} x = - \frac{1}{14}

Solution

x_{1} = - \frac{1}{14}, x_{2} = \frac{1}{14}

Alternative Form

x_{1} = - 0.0 \dot{7} 1428 \dot{5}, x_{2} = 0.0 \dot{7} 1428 \dot{5}

Show Solution