-16x^2+33.6x=10

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Solution for -16x^2+33.6x=10 equation:


Simplifying
-16x2 + 33.6x = 10

Reorder the terms:
33.6x + -16x2 = 10

Solving
33.6x + -16x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 33.6x + -16x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 33.6x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.625 + -2.1x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.1x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.1x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.1x + x2 = 0 + -0.625
-2.1x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.1x + x2 = -0.625

The x term is -2.1x.  Take half its coefficient (-1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
-2.1x + 1.1025 + x2 = -0.625 + 1.1025

Reorder the terms:
1.1025 + -2.1x + x2 = -0.625 + 1.1025

Combine like terms: -0.625 + 1.1025 = 0.4775
1.1025 + -2.1x + x2 = 0.4775

Factor a perfect square on the left side:
(x + -1.05)(x + -1.05) = 0.4775

Calculate the square root of the right side: 0.691013748

Break this problem into two subproblems by setting 
(x + -1.05) equal to 0.691013748 and -0.691013748.

Subproblem 1

x + -1.05 = 0.691013748 Simplifying x + -1.05 = 0.691013748 Reorder the terms: -1.05 + x = 0.691013748 Solving -1.05 + x = 0.691013748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 0.691013748 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 0.691013748 + 1.05 x = 0.691013748 + 1.05 Combine like terms: 0.691013748 + 1.05 = 1.741013748 x = 1.741013748 Simplifying x = 1.741013748

Subproblem 2

x + -1.05 = -0.691013748 Simplifying x + -1.05 = -0.691013748 Reorder the terms: -1.05 + x = -0.691013748 Solving -1.05 + x = -0.691013748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -0.691013748 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -0.691013748 + 1.05 x = -0.691013748 + 1.05 Combine like terms: -0.691013748 + 1.05 = 0.358986252 x = 0.358986252 Simplifying x = 0.358986252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.741013748, 0.358986252}

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