72x+4x^2=200

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Solution for 72x+4x^2=200 equation:


Simplifying
72x + 4x2 = 200

Solving
72x + 4x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + 72x + 4x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 18x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-50 + 18x + x2)' equal to zero and attempt to solve: Simplifying -50 + 18x + x2 = 0 Solving -50 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 18x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 18x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 18x + x2 = 0 + 50 18x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 18x + x2 = 50 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 50 + 81 Reorder the terms: 81 + 18x + x2 = 50 + 81 Combine like terms: 50 + 81 = 131 81 + 18x + x2 = 131 Factor a perfect square on the left side: (x + 9)(x + 9) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + 9) equal to 11.445523142 and -11.445523142.

Subproblem 1

x + 9 = 11.445523142 Simplifying x + 9 = 11.445523142 Reorder the terms: 9 + x = 11.445523142 Solving 9 + x = 11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 11.445523142 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.445523142 + -9 x = 11.445523142 + -9 Combine like terms: 11.445523142 + -9 = 2.445523142 x = 2.445523142 Simplifying x = 2.445523142

Subproblem 2

x + 9 = -11.445523142 Simplifying x + 9 = -11.445523142 Reorder the terms: 9 + x = -11.445523142 Solving 9 + x = -11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -11.445523142 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.445523142 + -9 x = -11.445523142 + -9 Combine like terms: -11.445523142 + -9 = -20.445523142 x = -20.445523142 Simplifying x = -20.445523142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.445523142, -20.445523142}

Solution

x = {2.445523142, -20.445523142}

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