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Simplifying -2.2 = (x * x) + -3.2x Multiply x * x -2.2 = (x2) + -3.2x -2.2 = x2 + -3.2x Reorder the terms: -2.2 = -3.2x + x2 Solving -2.2 = -3.2x + x2 Solving for variable 'x'. Reorder the terms: -2.2 + 3.2x + -1x2 = -3.2x + 3.2x + x2 + -1x2 Combine like terms: -3.2x + 3.2x = 0.0 -2.2 + 3.2x + -1x2 = 0.0 + x2 + -1x2 -2.2 + 3.2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2.2 + 3.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.2 + -3.2x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -3.2x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -3.2x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -3.2x + x2 = 0 + -2.2 -3.2x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -3.2x + x2 = -2.2 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 = -2.2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -2.2 + 2.56 Combine like terms: -2.2 + 2.56 = 0.36 2.56 + -3.2x + x2 = 0.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + -1.6) equal to 0.6 and -0.6.Subproblem 1
x + -1.6 = 0.6 Simplifying x + -1.6 = 0.6 Reorder the terms: -1.6 + x = 0.6 Solving -1.6 + x = 0.6 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 = 0.6 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 0.6 + 1.6 x = 0.6 + 1.6 Combine like terms: 0.6 + 1.6 = 2.2 x = 2.2 Simplifying x = 2.2Subproblem 2
x + -1.6 = -0.6 Simplifying x + -1.6 = -0.6 Reorder the terms: -1.6 + x = -0.6 Solving -1.6 + x = -0.6 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 = -0.6 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -0.6 + 1.6 x = -0.6 + 1.6 Combine like terms: -0.6 + 1.6 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2, 1}
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