0=-16x^2+91x+10

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Solution for 0=-16x^2+91x+10 equation:


Simplifying
0 = -16x2 + 91x + 10

Reorder the terms:
0 = 10 + 91x + -16x2

Solving
0 = 10 + 91x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -10 = -10
-10 + -91x + 16x2 = 10 + 91x + -16x2 + -10 + -91x + 16x2

Reorder the terms:
-10 + -91x + 16x2 = 10 + -10 + 91x + -91x + -16x2 + 16x2

Combine like terms: 10 + -10 = 0
-10 + -91x + 16x2 = 0 + 91x + -91x + -16x2 + 16x2
-10 + -91x + 16x2 = 91x + -91x + -16x2 + 16x2

Combine like terms: 91x + -91x = 0
-10 + -91x + 16x2 = 0 + -16x2 + 16x2
-10 + -91x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-10 + -91x + 16x2 = 0

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

Divide each side by '16'.
-0.625 + -5.6875x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -5.6875x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -5.6875x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -5.6875x + x2 = 0 + 0.625
-5.6875x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-5.6875x + x2 = 0.625

The x term is -5.6875x.  Take half its coefficient (-2.84375).
Square it (8.086914063) and add it to both sides.

Add '8.086914063' to each side of the equation.
-5.6875x + 8.086914063 + x2 = 0.625 + 8.086914063

Reorder the terms:
8.086914063 + -5.6875x + x2 = 0.625 + 8.086914063

Combine like terms: 0.625 + 8.086914063 = 8.711914063
8.086914063 + -5.6875x + x2 = 8.711914063

Factor a perfect square on the left side:
(x + -2.84375)(x + -2.84375) = 8.711914063

Calculate the square root of the right side: 2.951595173

Break this problem into two subproblems by setting 
(x + -2.84375) equal to 2.951595173 and -2.951595173.

Subproblem 1

x + -2.84375 = 2.951595173 Simplifying x + -2.84375 = 2.951595173 Reorder the terms: -2.84375 + x = 2.951595173 Solving -2.84375 + x = 2.951595173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.84375' to each side of the equation. -2.84375 + 2.84375 + x = 2.951595173 + 2.84375 Combine like terms: -2.84375 + 2.84375 = 0.00000 0.00000 + x = 2.951595173 + 2.84375 x = 2.951595173 + 2.84375 Combine like terms: 2.951595173 + 2.84375 = 5.795345173 x = 5.795345173 Simplifying x = 5.795345173

Subproblem 2

x + -2.84375 = -2.951595173 Simplifying x + -2.84375 = -2.951595173 Reorder the terms: -2.84375 + x = -2.951595173 Solving -2.84375 + x = -2.951595173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.84375' to each side of the equation. -2.84375 + 2.84375 + x = -2.951595173 + 2.84375 Combine like terms: -2.84375 + 2.84375 = 0.00000 0.00000 + x = -2.951595173 + 2.84375 x = -2.951595173 + 2.84375 Combine like terms: -2.951595173 + 2.84375 = -0.107845173 x = -0.107845173 Simplifying x = -0.107845173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.795345173, -0.107845173}

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