96x^2-8x-64=0

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Solution for 96x^2-8x-64=0 equation:


Simplifying
96x2 + -8x + -64 = 0

Reorder the terms:
-64 + -8x + 96x2 = 0

Solving
-64 + -8x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-8 + -1x + 12x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-8 + -1x + 12x2)' equal to zero and attempt to solve: Simplifying -8 + -1x + 12x2 = 0 Solving -8 + -1x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.08333333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.08333333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.08333333333x + x2 = 0 + 0.6666666667 -0.08333333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.08333333333x + x2 = 0.6666666667 The x term is -0.08333333333x. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333x + 0.001736111111 + x2 = 0.6666666667 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 0.6666666667 + 0.001736111111 Combine like terms: 0.6666666667 + 0.001736111111 = 0.668402777811 0.001736111111 + -0.08333333333x + x2 = 0.668402777811 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 0.668402777811 Calculate the square root of the right side: 0.817559036 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 0.817559036 and -0.817559036.

Subproblem 1

x + -0.04166666667 = 0.817559036 Simplifying x + -0.04166666667 = 0.817559036 Reorder the terms: -0.04166666667 + x = 0.817559036 Solving -0.04166666667 + x = 0.817559036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 0.817559036 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 0.817559036 + 0.04166666667 x = 0.817559036 + 0.04166666667 Combine like terms: 0.817559036 + 0.04166666667 = 0.85922570267 x = 0.85922570267 Simplifying x = 0.85922570267

Subproblem 2

x + -0.04166666667 = -0.817559036 Simplifying x + -0.04166666667 = -0.817559036 Reorder the terms: -0.04166666667 + x = -0.817559036 Solving -0.04166666667 + x = -0.817559036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -0.817559036 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -0.817559036 + 0.04166666667 x = -0.817559036 + 0.04166666667 Combine like terms: -0.817559036 + 0.04166666667 = -0.77589236933 x = -0.77589236933 Simplifying x = -0.77589236933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.85922570267, -0.77589236933}

Solution

x = {0.85922570267, -0.77589236933}

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