4(x^2+100x+600)=0

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Solution for 4(x^2+100x+600)=0 equation:


Simplifying
4(x2 + 100x + 600) = 0

Reorder the terms:
4(600 + 100x + x2) = 0
(600 * 4 + 100x * 4 + x2 * 4) = 0
(2400 + 400x + 4x2) = 0

Solving
2400 + 400x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(600 + 100x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(600 + 100x + x2)' equal to zero and attempt to solve: Simplifying 600 + 100x + x2 = 0 Solving 600 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + 100x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + 100x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + 100x + x2 = 0 + -600 100x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 100x + x2 = -600 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = -600 + 2500 Reorder the terms: 2500 + 100x + x2 = -600 + 2500 Combine like terms: -600 + 2500 = 1900 2500 + 100x + x2 = 1900 Factor a perfect square on the left side: (x + 50)(x + 50) = 1900 Calculate the square root of the right side: 43.588989435 Break this problem into two subproblems by setting (x + 50) equal to 43.588989435 and -43.588989435.

Subproblem 1

x + 50 = 43.588989435 Simplifying x + 50 = 43.588989435 Reorder the terms: 50 + x = 43.588989435 Solving 50 + x = 43.588989435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 43.588989435 + -50 Combine like terms: 50 + -50 = 0 0 + x = 43.588989435 + -50 x = 43.588989435 + -50 Combine like terms: 43.588989435 + -50 = -6.411010565 x = -6.411010565 Simplifying x = -6.411010565

Subproblem 2

x + 50 = -43.588989435 Simplifying x + 50 = -43.588989435 Reorder the terms: 50 + x = -43.588989435 Solving 50 + x = -43.588989435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -43.588989435 + -50 Combine like terms: 50 + -50 = 0 0 + x = -43.588989435 + -50 x = -43.588989435 + -50 Combine like terms: -43.588989435 + -50 = -93.588989435 x = -93.588989435 Simplifying x = -93.588989435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.411010565, -93.588989435}

Solution

x = {-6.411010565, -93.588989435}

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