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Simplifying -3.2x = 1.44 + -1x2 Solving -3.2x = 1.44 + -1x2 Solving for variable 'x'. Reorder the terms: -1.44 + -3.2x + x2 = 1.44 + -1x2 + -1.44 + x2 Reorder the terms: -1.44 + -3.2x + x2 = 1.44 + -1.44 + -1x2 + x2 Combine like terms: 1.44 + -1.44 = 0.00 -1.44 + -3.2x + x2 = 0.00 + -1x2 + x2 -1.44 + -3.2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1.44 + -3.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + -3.2x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + -3.2x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + -3.2x + x2 = 0 + 1.44 -3.2x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 -3.2x + x2 = 1.44 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 1.44 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 1.44 + 2.56 Combine like terms: 1.44 + 2.56 = 4 2.56 + -3.2x + x2 = 4 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -1.6) equal to 2 and -2.Subproblem 1
x + -1.6 = 2 Simplifying x + -1.6 = 2 Reorder the terms: -1.6 + x = 2 Solving -1.6 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2 + 1.6 x = 2 + 1.6 Combine like terms: 2 + 1.6 = 3.6 x = 3.6 Simplifying x = 3.6Subproblem 2
x + -1.6 = -2 Simplifying x + -1.6 = -2 Reorder the terms: -1.6 + x = -2 Solving -1.6 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2 + 1.6 x = -2 + 1.6 Combine like terms: -2 + 1.6 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6, -0.4}
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