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Simplifying 2x + 4x2 + -2 = 5x + -6x2 + 4 Reorder the terms: -2 + 2x + 4x2 = 5x + -6x2 + 4 Reorder the terms: -2 + 2x + 4x2 = 4 + 5x + -6x2 Solving -2 + 2x + 4x2 = 4 + 5x + -6x2 Solving for variable 'x'. Reorder the terms: -2 + -4 + 2x + -5x + 4x2 + 6x2 = 4 + 5x + -6x2 + -4 + -5x + 6x2 Combine like terms: -2 + -4 = -6 -6 + 2x + -5x + 4x2 + 6x2 = 4 + 5x + -6x2 + -4 + -5x + 6x2 Combine like terms: 2x + -5x = -3x -6 + -3x + 4x2 + 6x2 = 4 + 5x + -6x2 + -4 + -5x + 6x2 Combine like terms: 4x2 + 6x2 = 10x2 -6 + -3x + 10x2 = 4 + 5x + -6x2 + -4 + -5x + 6x2 Reorder the terms: -6 + -3x + 10x2 = 4 + -4 + 5x + -5x + -6x2 + 6x2 Combine like terms: 4 + -4 = 0 -6 + -3x + 10x2 = 0 + 5x + -5x + -6x2 + 6x2 -6 + -3x + 10x2 = 5x + -5x + -6x2 + 6x2 Combine like terms: 5x + -5x = 0 -6 + -3x + 10x2 = 0 + -6x2 + 6x2 -6 + -3x + 10x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -6 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.3x + 0.6 + x2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.3x + x2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.3x + x2 = 0.0 + 0.6 -0.3x + x2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -0.3x + x2 = 0.6 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.6 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.6 + 0.0225 Combine like terms: 0.6 + 0.0225 = 0.6225 0.0225 + -0.3x + x2 = 0.6225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.6225 Calculate the square root of the right side: 0.788986692 Break this problem into two subproblems by setting (x + -0.15) equal to 0.788986692 and -0.788986692.Subproblem 1
x + -0.15 = 0.788986692 Simplifying x + -0.15 = 0.788986692 Reorder the terms: -0.15 + x = 0.788986692 Solving -0.15 + x = 0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.788986692 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.788986692 + 0.15 x = 0.788986692 + 0.15 Combine like terms: 0.788986692 + 0.15 = 0.938986692 x = 0.938986692 Simplifying x = 0.938986692Subproblem 2
x + -0.15 = -0.788986692 Simplifying x + -0.15 = -0.788986692 Reorder the terms: -0.15 + x = -0.788986692 Solving -0.15 + x = -0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.788986692 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.788986692 + 0.15 x = -0.788986692 + 0.15 Combine like terms: -0.788986692 + 0.15 = -0.638986692 x = -0.638986692 Simplifying x = -0.638986692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.938986692, -0.638986692}
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