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Simplifying 2x2 + -2 = 0.5(x + 3) Reorder the terms: -2 + 2x2 = 0.5(x + 3) Reorder the terms: -2 + 2x2 = 0.5(3 + x) -2 + 2x2 = (3 * 0.5 + x * 0.5) -2 + 2x2 = (1.5 + 0.5x) Solving -2 + 2x2 = 1.5 + 0.5x Solving for variable 'x'. Reorder the terms: -2 + -1.5 + -0.5x + 2x2 = 1.5 + 0.5x + -1.5 + -0.5x Combine like terms: -2 + -1.5 = -3.5 -3.5 + -0.5x + 2x2 = 1.5 + 0.5x + -1.5 + -0.5x Reorder the terms: -3.5 + -0.5x + 2x2 = 1.5 + -1.5 + 0.5x + -0.5x Combine like terms: 1.5 + -1.5 = 0.0 -3.5 + -0.5x + 2x2 = 0.0 + 0.5x + -0.5x -3.5 + -0.5x + 2x2 = 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 -3.5 + -0.5x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.75 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.25x + 1.75 + x2 = 0.0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.25x + x2 = 0.0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.25x + x2 = 0.0 + 1.75 -0.25x + x2 = 0.0 + 1.75 Combine like terms: 0.0 + 1.75 = 1.75 -0.25x + x2 = 1.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 1.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 1.75 + 0.015625 Combine like terms: 1.75 + 0.015625 = 1.765625 0.015625 + -0.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + -0.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x + -0.125 = 1.328768227 Simplifying x + -0.125 = 1.328768227 Reorder the terms: -0.125 + x = 1.328768227 Solving -0.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.328768227 + 0.125 x = 1.328768227 + 0.125 Combine like terms: 1.328768227 + 0.125 = 1.453768227 x = 1.453768227 Simplifying x = 1.453768227Subproblem 2
x + -0.125 = -1.328768227 Simplifying x + -0.125 = -1.328768227 Reorder the terms: -0.125 + x = -1.328768227 Solving -0.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.328768227 + 0.125 x = -1.328768227 + 0.125 Combine like terms: -1.328768227 + 0.125 = -1.203768227 x = -1.203768227 Simplifying x = -1.203768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.453768227, -1.203768227}
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