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Simplifying 2x * x = x + 12x + 3 Multiply x * x 2x2 = x + 12x + 3 Reorder the terms: 2x2 = 3 + x + 12x Combine like terms: x + 12x = 13x 2x2 = 3 + 13x Solving 2x2 = 3 + 13x Solving for variable 'x'. Reorder the terms: -3 + -13x + 2x2 = 3 + 13x + -3 + -13x Reorder the terms: -3 + -13x + 2x2 = 3 + -3 + 13x + -13x Combine like terms: 3 + -3 = 0 -3 + -13x + 2x2 = 0 + 13x + -13x -3 + -13x + 2x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -3 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -6.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -6.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -6.5x + x2 = 0 + 1.5 -6.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -6.5x + x2 = 1.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 1.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 1.5 + 10.5625 Combine like terms: 1.5 + 10.5625 = 12.0625 10.5625 + -6.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -3.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -3.25 = 3.473110997 Simplifying x + -3.25 = 3.473110997 Reorder the terms: -3.25 + x = 3.473110997 Solving -3.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.473110997 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.473110997 + 3.25 x = 3.473110997 + 3.25 Combine like terms: 3.473110997 + 3.25 = 6.723110997 x = 6.723110997 Simplifying x = 6.723110997Subproblem 2
x + -3.25 = -3.473110997 Simplifying x + -3.25 = -3.473110997 Reorder the terms: -3.25 + x = -3.473110997 Solving -3.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.473110997 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.473110997 + 3.25 x = -3.473110997 + 3.25 Combine like terms: -3.473110997 + 3.25 = -0.223110997 x = -0.223110997 Simplifying x = -0.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.723110997, -0.223110997}
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