100=-16x^2+95x+8

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Solution for 100=-16x^2+95x+8 equation:


Simplifying
100 = -16x2 + 95x + 8

Reorder the terms:
100 = 8 + 95x + -16x2

Solving
100 = 8 + 95x + -16x2

Solving for variable 'x'.

Combine like terms: 100 + -8 = 92
92 + -95x + 16x2 = 8 + 95x + -16x2 + -8 + -95x + 16x2

Reorder the terms:
92 + -95x + 16x2 = 8 + -8 + 95x + -95x + -16x2 + 16x2

Combine like terms: 8 + -8 = 0
92 + -95x + 16x2 = 0 + 95x + -95x + -16x2 + 16x2
92 + -95x + 16x2 = 95x + -95x + -16x2 + 16x2

Combine like terms: 95x + -95x = 0
92 + -95x + 16x2 = 0 + -16x2 + 16x2
92 + -95x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
92 + -95x + 16x2 = 0

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

Divide each side by '16'.
5.75 + -5.9375x + x2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + -5.9375x + -5.75 + x2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + -5.9375x + x2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + -5.9375x + x2 = 0 + -5.75
-5.9375x + x2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
-5.9375x + x2 = -5.75

The x term is -5.9375x.  Take half its coefficient (-2.96875).
Square it (8.813476563) and add it to both sides.

Add '8.813476563' to each side of the equation.
-5.9375x + 8.813476563 + x2 = -5.75 + 8.813476563

Reorder the terms:
8.813476563 + -5.9375x + x2 = -5.75 + 8.813476563

Combine like terms: -5.75 + 8.813476563 = 3.063476563
8.813476563 + -5.9375x + x2 = 3.063476563

Factor a perfect square on the left side:
(x + -2.96875)(x + -2.96875) = 3.063476563

Calculate the square root of the right side: 1.750278996

Break this problem into two subproblems by setting 
(x + -2.96875) equal to 1.750278996 and -1.750278996.

Subproblem 1

x + -2.96875 = 1.750278996 Simplifying x + -2.96875 = 1.750278996 Reorder the terms: -2.96875 + x = 1.750278996 Solving -2.96875 + x = 1.750278996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 1.750278996 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 1.750278996 + 2.96875 x = 1.750278996 + 2.96875 Combine like terms: 1.750278996 + 2.96875 = 4.719028996 x = 4.719028996 Simplifying x = 4.719028996

Subproblem 2

x + -2.96875 = -1.750278996 Simplifying x + -2.96875 = -1.750278996 Reorder the terms: -2.96875 + x = -1.750278996 Solving -2.96875 + x = -1.750278996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -1.750278996 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -1.750278996 + 2.96875 x = -1.750278996 + 2.96875 Combine like terms: -1.750278996 + 2.96875 = 1.218471004 x = 1.218471004 Simplifying x = 1.218471004

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.719028996, 1.218471004}

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