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Simplifying 12x(x + 2) = 12x + 2 Reorder the terms: 12x(2 + x) = 12x + 2 (2 * 12x + x * 12x) = 12x + 2 (24x + 12x2) = 12x + 2 Reorder the terms: 24x + 12x2 = 2 + 12x Solving 24x + 12x2 = 2 + 12x Solving for variable 'x'. Reorder the terms: -2 + 24x + -12x + 12x2 = 2 + 12x + -2 + -12x Combine like terms: 24x + -12x = 12x -2 + 12x + 12x2 = 2 + 12x + -2 + -12x Reorder the terms: -2 + 12x + 12x2 = 2 + -2 + 12x + -12x Combine like terms: 2 + -2 = 0 -2 + 12x + 12x2 = 0 + 12x + -12x -2 + 12x + 12x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -2 + 12x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 6x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 6x + 6x2)' equal to zero and attempt to solve: Simplifying -1 + 6x + 6x2 = 0 Solving -1 + 6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.1666666667 x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 x + x2 = 0.1666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.1666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.1666666667 + 0.25 Combine like terms: 0.1666666667 + 0.25 = 0.4166666667 1.25 + x2 = 0.4166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4166666667 Calculate the square root of the right side: 0.645497224 Break this problem into two subproblems by setting (x + 0.5) equal to 0.645497224 and -0.645497224.Subproblem 1
x + 0.5 = 0.645497224 Simplifying x + 0.5 = 0.645497224 Reorder the terms: 0.5 + x = 0.645497224 Solving 0.5 + x = 0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.645497224 + -0.5 x = 0.645497224 + -0.5 Combine like terms: 0.645497224 + -0.5 = 0.145497224 x = 0.145497224 Simplifying x = 0.145497224Subproblem 2
x + 0.5 = -0.645497224 Simplifying x + 0.5 = -0.645497224 Reorder the terms: 0.5 + x = -0.645497224 Solving 0.5 + x = -0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.645497224 + -0.5 x = -0.645497224 + -0.5 Combine like terms: -0.645497224 + -0.5 = -1.145497224 x = -1.145497224 Simplifying x = -1.145497224Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.145497224, -1.145497224}Solution
x = {0.145497224, -1.145497224}
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