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Simplifying (x + -3)(x + -0.6) = 0 Reorder the terms: (-3 + x)(x + -0.6) = 0 Reorder the terms: (-3 + x)(-0.6 + x) = 0 Multiply (-3 + x) * (-0.6 + x) (-3(-0.6 + x) + x(-0.6 + x)) = 0 ((-0.6 * -3 + x * -3) + x(-0.6 + x)) = 0 ((1.8 + -3x) + x(-0.6 + x)) = 0 (1.8 + -3x + (-0.6 * x + x * x)) = 0 (1.8 + -3x + (-0.6x + x2)) = 0 Combine like terms: -3x + -0.6x = -3.6x (1.8 + -3.6x + x2) = 0 Solving 1.8 + -3.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -3.6x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -3.6x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -3.6x + x2 = 0 + -1.8 -3.6x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -3.6x + x2 = -1.8 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -1.8 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -1.8 + 3.24 Combine like terms: -1.8 + 3.24 = 1.44 3.24 + -3.6x + x2 = 1.44 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 1.44 Calculate the square root of the right side: 1.2 Break this problem into two subproblems by setting (x + -1.8) equal to 1.2 and -1.2.Subproblem 1
x + -1.8 = 1.2 Simplifying x + -1.8 = 1.2 Reorder the terms: -1.8 + x = 1.2 Solving -1.8 + x = 1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.2 + 1.8 x = 1.2 + 1.8 Combine like terms: 1.2 + 1.8 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.8 = -1.2 Simplifying x + -1.8 = -1.2 Reorder the terms: -1.8 + x = -1.2 Solving -1.8 + x = -1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.2 + 1.8 x = -1.2 + 1.8 Combine like terms: -1.2 + 1.8 = 0.6 x = 0.6 Simplifying x = 0.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 0.6}
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