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Simplifying (x + -3)(2.2 + x) = 0 Reorder the terms: (-3 + x)(2.2 + x) = 0 Multiply (-3 + x) * (2.2 + x) (-3(2.2 + x) + x(2.2 + x)) = 0 ((2.2 * -3 + x * -3) + x(2.2 + x)) = 0 ((-6.6 + -3x) + x(2.2 + x)) = 0 (-6.6 + -3x + (2.2 * x + x * x)) = 0 (-6.6 + -3x + (2.2x + x2)) = 0 Combine like terms: -3x + 2.2x = -0.8x (-6.6 + -0.8x + x2) = 0 Solving -6.6 + -0.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -0.8x + 6.6 + x2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -0.8x + x2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -0.8x + x2 = 0 + 6.6 -0.8x + x2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -0.8x + x2 = 6.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 6.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 6.6 + 0.16 Combine like terms: 6.6 + 0.16 = 6.76 0.16 + -0.8x + x2 = 6.76 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 6.76 Calculate the square root of the right side: 2.6 Break this problem into two subproblems by setting (x + -0.4) equal to 2.6 and -2.6.Subproblem 1
x + -0.4 = 2.6 Simplifying x + -0.4 = 2.6 Reorder the terms: -0.4 + x = 2.6 Solving -0.4 + x = 2.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 2.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 2.6 + 0.4 x = 2.6 + 0.4 Combine like terms: 2.6 + 0.4 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -0.4 = -2.6 Simplifying x + -0.4 = -2.6 Reorder the terms: -0.4 + x = -2.6 Solving -0.4 + x = -2.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -2.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -2.6 + 0.4 x = -2.6 + 0.4 Combine like terms: -2.6 + 0.4 = -2.2 x = -2.2 Simplifying x = -2.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -2.2}
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