0=4x^2+120x+400

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Solution for 0=4x^2+120x+400 equation:


Simplifying
0 = 4x2 + 120x + 400

Reorder the terms:
0 = 400 + 120x + 4x2

Solving
0 = 400 + 120x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -400 = -400
-400 + -120x + -4x2 = 400 + 120x + 4x2 + -400 + -120x + -4x2

Reorder the terms:
-400 + -120x + -4x2 = 400 + -400 + 120x + -120x + 4x2 + -4x2

Combine like terms: 400 + -400 = 0
-400 + -120x + -4x2 = 0 + 120x + -120x + 4x2 + -4x2
-400 + -120x + -4x2 = 120x + -120x + 4x2 + -4x2

Combine like terms: 120x + -120x = 0
-400 + -120x + -4x2 = 0 + 4x2 + -4x2
-400 + -120x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-400 + -120x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(100 + 30x + x2) = 0

Ignore the factor -4.

Subproblem 1

Set the factor '(100 + 30x + x2)' equal to zero and attempt to solve: Simplifying 100 + 30x + x2 = 0 Solving 100 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 30x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 30x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 30x + x2 = 0 + -100 30x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 30x + x2 = -100 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -100 + 225 Reorder the terms: 225 + 30x + x2 = -100 + 225 Combine like terms: -100 + 225 = 125 225 + 30x + x2 = 125 Factor a perfect square on the left side: (x + 15)(x + 15) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 15) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + 15 = 11.180339887 Simplifying x + 15 = 11.180339887 Reorder the terms: 15 + x = 11.180339887 Solving 15 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 11.180339887 + -15 Combine like terms: 15 + -15 = 0 0 + x = 11.180339887 + -15 x = 11.180339887 + -15 Combine like terms: 11.180339887 + -15 = -3.819660113 x = -3.819660113 Simplifying x = -3.819660113

Subproblem 2

x + 15 = -11.180339887 Simplifying x + 15 = -11.180339887 Reorder the terms: 15 + x = -11.180339887 Solving 15 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -11.180339887 + -15 Combine like terms: 15 + -15 = 0 0 + x = -11.180339887 + -15 x = -11.180339887 + -15 Combine like terms: -11.180339887 + -15 = -26.180339887 x = -26.180339887 Simplifying x = -26.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.819660113, -26.180339887}

Solution

x = {-3.819660113, -26.180339887}

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