64x^2+144x+81=10

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Solution for 64x^2+144x+81=10 equation:


Simplifying
64x2 + 144x + 81 = 10

Reorder the terms:
81 + 144x + 64x2 = 10

Solving
81 + 144x + 64x2 = 10

Solving for variable 'x'.

Reorder the terms:
81 + -10 + 144x + 64x2 = 10 + -10

Combine like terms: 81 + -10 = 71
71 + 144x + 64x2 = 10 + -10

Combine like terms: 10 + -10 = 0
71 + 144x + 64x2 = 0

Begin completing the square.  Divide all terms by
64 the coefficient of the squared term: 

Divide each side by '64'.
1.109375 + 2.25x + x2 = 0

Move the constant term to the right:

Add '-1.109375' to each side of the equation.
1.109375 + 2.25x + -1.109375 + x2 = 0 + -1.109375

Reorder the terms:
1.109375 + -1.109375 + 2.25x + x2 = 0 + -1.109375

Combine like terms: 1.109375 + -1.109375 = 0.000000
0.000000 + 2.25x + x2 = 0 + -1.109375
2.25x + x2 = 0 + -1.109375

Combine like terms: 0 + -1.109375 = -1.109375
2.25x + x2 = -1.109375

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = -1.109375 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = -1.109375 + 1.265625

Combine like terms: -1.109375 + 1.265625 = 0.15625
1.265625 + 2.25x + x2 = 0.15625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 0.15625

Calculate the square root of the right side: 0.395284708

Break this problem into two subproblems by setting 
(x + 1.125) equal to 0.395284708 and -0.395284708.

Subproblem 1

x + 1.125 = 0.395284708 Simplifying x + 1.125 = 0.395284708 Reorder the terms: 1.125 + x = 0.395284708 Solving 1.125 + x = 0.395284708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.395284708 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.395284708 + -1.125 x = 0.395284708 + -1.125 Combine like terms: 0.395284708 + -1.125 = -0.729715292 x = -0.729715292 Simplifying x = -0.729715292

Subproblem 2

x + 1.125 = -0.395284708 Simplifying x + 1.125 = -0.395284708 Reorder the terms: 1.125 + x = -0.395284708 Solving 1.125 + x = -0.395284708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.395284708 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.395284708 + -1.125 x = -0.395284708 + -1.125 Combine like terms: -0.395284708 + -1.125 = -1.520284708 x = -1.520284708 Simplifying x = -1.520284708

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.729715292, -1.520284708}

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