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Simplifying x2 + (3x + -1)(3x + -1) = 16 Reorder the terms: x2 + (-1 + 3x)(3x + -1) = 16 Reorder the terms: x2 + (-1 + 3x)(-1 + 3x) = 16 Multiply (-1 + 3x) * (-1 + 3x) x2 + (-1(-1 + 3x) + 3x * (-1 + 3x)) = 16 x2 + ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 16 x2 + ((1 + -3x) + 3x * (-1 + 3x)) = 16 x2 + (1 + -3x + (-1 * 3x + 3x * 3x)) = 16 x2 + (1 + -3x + (-3x + 9x2)) = 16 Combine like terms: -3x + -3x = -6x x2 + (1 + -6x + 9x2) = 16 Reorder the terms: 1 + -6x + x2 + 9x2 = 16 Combine like terms: x2 + 9x2 = 10x2 1 + -6x + 10x2 = 16 Solving 1 + -6x + 10x2 = 16 Solving for variable 'x'. Reorder the terms: 1 + -16 + -6x + 10x2 = 16 + -16 Combine like terms: 1 + -16 = -15 -15 + -6x + 10x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -15 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.6x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.6x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.6x + x2 = 0.0 + 1.5 -0.6x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -0.6x + x2 = 1.5 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.5 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.5 + 0.09 Combine like terms: 1.5 + 0.09 = 1.59 0.09 + -0.6x + x2 = 1.59 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.59 Calculate the square root of the right side: 1.260952021 Break this problem into two subproblems by setting (x + -0.3) equal to 1.260952021 and -1.260952021.Subproblem 1
x + -0.3 = 1.260952021 Simplifying x + -0.3 = 1.260952021 Reorder the terms: -0.3 + x = 1.260952021 Solving -0.3 + x = 1.260952021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.260952021 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.260952021 + 0.3 x = 1.260952021 + 0.3 Combine like terms: 1.260952021 + 0.3 = 1.560952021 x = 1.560952021 Simplifying x = 1.560952021Subproblem 2
x + -0.3 = -1.260952021 Simplifying x + -0.3 = -1.260952021 Reorder the terms: -0.3 + x = -1.260952021 Solving -0.3 + x = -1.260952021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.260952021 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.260952021 + 0.3 x = -1.260952021 + 0.3 Combine like terms: -1.260952021 + 0.3 = -0.960952021 x = -0.960952021 Simplifying x = -0.960952021Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560952021, -0.960952021}
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