2x^2+12x=200

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Solution for 2x^2+12x=200 equation:


Simplifying
2x2 + 12x = 200

Reorder the terms:
12x + 2x2 = 200

Solving
12x + 2x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + 12x + 2x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-100 + 6x + x2)' equal to zero and attempt to solve: Simplifying -100 + 6x + x2 = 0 Solving -100 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 6x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 6x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 6x + x2 = 0 + 100 6x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 6x + x2 = 100 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 100 + 9 Reorder the terms: 9 + 6x + x2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + 6x + x2 = 109 Factor a perfect square on the left side: (x + 3)(x + 3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 3) equal to 10.440306509 and -10.440306509.

Subproblem 1

x + 3 = 10.440306509 Simplifying x + 3 = 10.440306509 Reorder the terms: 3 + x = 10.440306509 Solving 3 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.440306509 + -3 x = 10.440306509 + -3 Combine like terms: 10.440306509 + -3 = 7.440306509 x = 7.440306509 Simplifying x = 7.440306509

Subproblem 2

x + 3 = -10.440306509 Simplifying x + 3 = -10.440306509 Reorder the terms: 3 + x = -10.440306509 Solving 3 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.440306509 + -3 x = -10.440306509 + -3 Combine like terms: -10.440306509 + -3 = -13.440306509 x = -13.440306509 Simplifying x = -13.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.440306509, -13.440306509}

Solution

x = {7.440306509, -13.440306509}

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