x=-16(x^2)+48x+160

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Solution for x=-16(x^2)+48x+160 equation:


Simplifying
x = -16(x2) + 48x + 160

Reorder the terms:
x = 160 + 48x + -16x2

Solving
x = 160 + 48x + -16x2

Solving for variable 'x'.

Reorder the terms:
-160 + x + -48x + 16x2 = 160 + 48x + -16x2 + -160 + -48x + 16x2

Combine like terms: x + -48x = -47x
-160 + -47x + 16x2 = 160 + 48x + -16x2 + -160 + -48x + 16x2

Reorder the terms:
-160 + -47x + 16x2 = 160 + -160 + 48x + -48x + -16x2 + 16x2

Combine like terms: 160 + -160 = 0
-160 + -47x + 16x2 = 0 + 48x + -48x + -16x2 + 16x2
-160 + -47x + 16x2 = 48x + -48x + -16x2 + 16x2

Combine like terms: 48x + -48x = 0
-160 + -47x + 16x2 = 0 + -16x2 + 16x2
-160 + -47x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-160 + -47x + 16x2 = 0

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

Divide each side by '16'.
-10 + -2.9375x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2.9375x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -2.9375x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2.9375x + x2 = 0 + 10
-2.9375x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2.9375x + x2 = 10

The x term is -2.9375x.  Take half its coefficient (-1.46875).
Square it (2.157226563) and add it to both sides.

Add '2.157226563' to each side of the equation.
-2.9375x + 2.157226563 + x2 = 10 + 2.157226563

Reorder the terms:
2.157226563 + -2.9375x + x2 = 10 + 2.157226563

Combine like terms: 10 + 2.157226563 = 12.157226563
2.157226563 + -2.9375x + x2 = 12.157226563

Factor a perfect square on the left side:
(x + -1.46875)(x + -1.46875) = 12.157226563

Calculate the square root of the right side: 3.486721463

Break this problem into two subproblems by setting 
(x + -1.46875) equal to 3.486721463 and -3.486721463.

Subproblem 1

x + -1.46875 = 3.486721463 Simplifying x + -1.46875 = 3.486721463 Reorder the terms: -1.46875 + x = 3.486721463 Solving -1.46875 + x = 3.486721463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + x = 3.486721463 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + x = 3.486721463 + 1.46875 x = 3.486721463 + 1.46875 Combine like terms: 3.486721463 + 1.46875 = 4.955471463 x = 4.955471463 Simplifying x = 4.955471463

Subproblem 2

x + -1.46875 = -3.486721463 Simplifying x + -1.46875 = -3.486721463 Reorder the terms: -1.46875 + x = -3.486721463 Solving -1.46875 + x = -3.486721463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + x = -3.486721463 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + x = -3.486721463 + 1.46875 x = -3.486721463 + 1.46875 Combine like terms: -3.486721463 + 1.46875 = -2.017971463 x = -2.017971463 Simplifying x = -2.017971463

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.955471463, -2.017971463}

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