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Simplifying 204 = 6x2 + 12x + 4 Reorder the terms: 204 = 4 + 12x + 6x2 Solving 204 = 4 + 12x + 6x2 Solving for variable 'x'. Combine like terms: 204 + -4 = 200 200 + -12x + -6x2 = 4 + 12x + 6x2 + -4 + -12x + -6x2 Reorder the terms: 200 + -12x + -6x2 = 4 + -4 + 12x + -12x + 6x2 + -6x2 Combine like terms: 4 + -4 = 0 200 + -12x + -6x2 = 0 + 12x + -12x + 6x2 + -6x2 200 + -12x + -6x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 200 + -12x + -6x2 = 0 + 6x2 + -6x2 200 + -12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 200 + -12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -6x + -3x2)' equal to zero and attempt to solve: Simplifying 100 + -6x + -3x2 = 0 Solving 100 + -6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -33.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 2x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 2x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 33.33333333 2x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 2x + x2 = 33.33333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 33.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 33.33333333 + 1 Combine like terms: 33.33333333 + 1 = 34.33333333 1 + 2x + x2 = 34.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 34.33333333 Calculate the square root of the right side: 5.859465277 Break this problem into two subproblems by setting (x + 1) equal to 5.859465277 and -5.859465277.Subproblem 1
x + 1 = 5.859465277 Simplifying x + 1 = 5.859465277 Reorder the terms: 1 + x = 5.859465277 Solving 1 + x = 5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.859465277 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.859465277 + -1 x = 5.859465277 + -1 Combine like terms: 5.859465277 + -1 = 4.859465277 x = 4.859465277 Simplifying x = 4.859465277Subproblem 2
x + 1 = -5.859465277 Simplifying x + 1 = -5.859465277 Reorder the terms: 1 + x = -5.859465277 Solving 1 + x = -5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.859465277 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.859465277 + -1 x = -5.859465277 + -1 Combine like terms: -5.859465277 + -1 = -6.859465277 x = -6.859465277 Simplifying x = -6.859465277Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.859465277, -6.859465277}Solution
x = {4.859465277, -6.859465277}
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