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Simplifying 2x(5x + -10) = (x + 2) + -6x Reorder the terms: 2x(-10 + 5x) = (x + 2) + -6x (-10 * 2x + 5x * 2x) = (x + 2) + -6x (-20x + 10x2) = (x + 2) + -6x Reorder the terms: -20x + 10x2 = (2 + x) + -6x Remove parenthesis around (2 + x) -20x + 10x2 = 2 + x + -6x Combine like terms: x + -6x = -5x -20x + 10x2 = 2 + -5x Solving -20x + 10x2 = 2 + -5x Solving for variable 'x'. Reorder the terms: -2 + -20x + 5x + 10x2 = 2 + -5x + -2 + 5x Combine like terms: -20x + 5x = -15x -2 + -15x + 10x2 = 2 + -5x + -2 + 5x Reorder the terms: -2 + -15x + 10x2 = 2 + -2 + -5x + 5x Combine like terms: 2 + -2 = 0 -2 + -15x + 10x2 = 0 + -5x + 5x -2 + -15x + 10x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -2 + -15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -1.5x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.5x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.5x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.5x + x2 = 0.0 + 0.2 -1.5x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -1.5x + x2 = 0.2 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.2 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.2 + 0.5625 Combine like terms: 0.2 + 0.5625 = 0.7625 0.5625 + -1.5x + x2 = 0.7625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.7625 Calculate the square root of the right side: 0.87321246 Break this problem into two subproblems by setting (x + -0.75) equal to 0.87321246 and -0.87321246.Subproblem 1
x + -0.75 = 0.87321246 Simplifying x + -0.75 = 0.87321246 Reorder the terms: -0.75 + x = 0.87321246 Solving -0.75 + x = 0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.87321246 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.87321246 + 0.75 x = 0.87321246 + 0.75 Combine like terms: 0.87321246 + 0.75 = 1.62321246 x = 1.62321246 Simplifying x = 1.62321246Subproblem 2
x + -0.75 = -0.87321246 Simplifying x + -0.75 = -0.87321246 Reorder the terms: -0.75 + x = -0.87321246 Solving -0.75 + x = -0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.87321246 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.87321246 + 0.75 x = -0.87321246 + 0.75 Combine like terms: -0.87321246 + 0.75 = -0.12321246 x = -0.12321246 Simplifying x = -0.12321246Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.62321246, -0.12321246}
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