Solve 4x^2 34x - 28=0

Question

Solve the equation

x = \frac{3 8092}{34}

Alternative Form

x \approx 0.590482

Evaluate

4 x^{2} \times 34 x - 28 = 0

Multiply

More Steps

Evaluate

4 x^{2} \times 34 x

Multiply the terms

136 x^{2} \times x

Multiply the terms with the same base by adding their exponents

136 x^{2 + 1}

Add the numbers

136 x^{3}

136 x^{3} - 28 = 0

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

136 x^{3} = 0 + 28

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

136 x^{3} = 28

Divide both sides

\frac{136 x ^{3}}{136} = \frac{28}{136}

Divide the numbers

x^{3} = \frac{28}{136}

Cancel out the common factor 4

x^{3} = \frac{7}{34}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{7}{34}

Calculate

x = 3 \frac{7}{34}

Solution

More Steps

Evaluate

3 \frac{7}{34}

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

\frac{3 7}{3 34}

Multiply by the Conjugate

\frac{3 7 \times 3 3 4 ^{2}}{3 34 \times 3 3 4 ^{2}}

Simplify

\frac{3 7 \times 3 1156}{3 34 \times 3 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 31156

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

3 7 \times 1156

Calculate the product

38092

\frac{3 8092}{3 34 \times 3 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

334 \times 3 3 4^{2}

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

3 34 \times 3 4^{2}

Calculate the product

3 3 4^{3}

Reduce the index of the radical and exponent with 3

34

\frac{3 8092}{34}

x = \frac{3 8092}{34}

Alternative Form

x \approx 0.590482

Show Solution