0=4x^2-180x+160

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Solution for 0=4x^2-180x+160 equation:


Simplifying
0 = 4x2 + -180x + 160

Reorder the terms:
0 = 160 + -180x + 4x2

Solving
0 = 160 + -180x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -160 = -160
-160 + 180x + -4x2 = 160 + -180x + 4x2 + -160 + 180x + -4x2

Reorder the terms:
-160 + 180x + -4x2 = 160 + -160 + -180x + 180x + 4x2 + -4x2

Combine like terms: 160 + -160 = 0
-160 + 180x + -4x2 = 0 + -180x + 180x + 4x2 + -4x2
-160 + 180x + -4x2 = -180x + 180x + 4x2 + -4x2

Combine like terms: -180x + 180x = 0
-160 + 180x + -4x2 = 0 + 4x2 + -4x2
-160 + 180x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-160 + 180x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 45x + -1x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-40 + 45x + -1x2)' equal to zero and attempt to solve: Simplifying -40 + 45x + -1x2 = 0 Solving -40 + 45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -45x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -45x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -45x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -45x + x2 = 0 + -40 -45x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -45x + x2 = -40 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -40 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -40 + 506.25 Combine like terms: -40 + 506.25 = 466.25 506.25 + -45x + x2 = 466.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 466.25 Calculate the square root of the right side: 21.592822882 Break this problem into two subproblems by setting (x + -22.5) equal to 21.592822882 and -21.592822882.

Subproblem 1

x + -22.5 = 21.592822882 Simplifying x + -22.5 = 21.592822882 Reorder the terms: -22.5 + x = 21.592822882 Solving -22.5 + x = 21.592822882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 21.592822882 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 21.592822882 + 22.5 x = 21.592822882 + 22.5 Combine like terms: 21.592822882 + 22.5 = 44.092822882 x = 44.092822882 Simplifying x = 44.092822882

Subproblem 2

x + -22.5 = -21.592822882 Simplifying x + -22.5 = -21.592822882 Reorder the terms: -22.5 + x = -21.592822882 Solving -22.5 + x = -21.592822882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -21.592822882 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -21.592822882 + 22.5 x = -21.592822882 + 22.5 Combine like terms: -21.592822882 + 22.5 = 0.907177118 x = 0.907177118 Simplifying x = 0.907177118

Solution

The solution to the problem is based on the solutions from the subproblems. x = {44.092822882, 0.907177118}

Solution

x = {44.092822882, 0.907177118}

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