Solve 3x² + x + 10 = 0. Round solutions to the nearest hundredth.

Solution:

Given,

3x² + x + 10 = 0.

For using complete square method, the equation must be in the from

x² + bx =c.

3x² + x + 10 = 0.

Subtract 10 from both sides of the equation.

3x² + x = -10.

Divide both sides by 3.

3x² + x/3 = -10/3

Dividing by 3 undoes the multiplication of 3.

x² + 1/3x = -10/3.

Making the equation a perfect square,

x² +1/3x + (1/6)² = -10/3 + (1/6)²

Squaring we get,

x² + 1/3x + 1/36 = -10/3 + 1/36

x² +1/3x + 1/36 = -119/36

Factoring, we get,

(x + 1/6)² = -119/36

Taking square root on both sides,

√(x + 1/6)² =√-119/36

Simplifying we get,

x + 1/6 = √119i/6

x + 1/6 = - √119i/6

Subtracting 1/6 from both sides,

x = (-1 + √119i)/6

x = (- √119i - 1)/6

x = (-1 +√119i)/6 ≈ 1.818i

x = (- √119i - 1)/6 ≈ 1.818i

Therefore, the solution is 1.818i.

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Solve 3x² + x + 10 = 0. Round solutions to the nearest hundredth.

Summary:

Solving 3x² + x + 10 = 0 the solutions to the nearest hundredth is 1.818i