7=-16x^2+96x

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Solution for 7=-16x^2+96x equation:


Simplifying
7 = -16x2 + 96x

Reorder the terms:
7 = 96x + -16x2

Solving
7 = 96x + -16x2

Solving for variable 'x'.

Reorder the terms:
7 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2

Combine like terms: 96x + -96x = 0
7 + -96x + 16x2 = 0 + -16x2 + 16x2
7 + -96x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
7 + -96x + 16x2 = 0

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

Divide each side by '16'.
0.4375 + -6x + x2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -6x + -0.4375 + x2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -6x + x2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -6x + x2 = 0 + -0.4375
-6x + x2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-6x + x2 = -0.4375

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -0.4375 + 9

Reorder the terms:
9 + -6x + x2 = -0.4375 + 9

Combine like terms: -0.4375 + 9 = 8.5625
9 + -6x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -3) equal to 2.926174978 and -2.926174978.

Subproblem 1

x + -3 = 2.926174978 Simplifying x + -3 = 2.926174978 Reorder the terms: -3 + x = 2.926174978 Solving -3 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.926174978 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.926174978 + 3 x = 2.926174978 + 3 Combine like terms: 2.926174978 + 3 = 5.926174978 x = 5.926174978 Simplifying x = 5.926174978

Subproblem 2

x + -3 = -2.926174978 Simplifying x + -3 = -2.926174978 Reorder the terms: -3 + x = -2.926174978 Solving -3 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.926174978 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.926174978 + 3 x = -2.926174978 + 3 Combine like terms: -2.926174978 + 3 = 0.073825022 x = 0.073825022 Simplifying x = 0.073825022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.926174978, 0.073825022}

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