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Simplifying (x + 0.8)(x + -2) = 0 Reorder the terms: (0.8 + x)(x + -2) = 0 Reorder the terms: (0.8 + x)(-2 + x) = 0 Multiply (0.8 + x) * (-2 + x) (0.8(-2 + x) + x(-2 + x)) = 0 ((-2 * 0.8 + x * 0.8) + x(-2 + x)) = 0 ((-1.6 + 0.8x) + x(-2 + x)) = 0 (-1.6 + 0.8x + (-2 * x + x * x)) = 0 (-1.6 + 0.8x + (-2x + x2)) = 0 Combine like terms: 0.8x + -2x = -1.2x (-1.6 + -1.2x + x2) = 0 Solving -1.6 + -1.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.2x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.2x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.2x + x2 = 0 + 1.6 -1.2x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.2x + x2 = 1.6 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 1.6 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.6 + 0.36 Combine like terms: 1.6 + 0.36 = 1.96 0.36 + -1.2x + x2 = 1.96 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.96 Calculate the square root of the right side: 1.4 Break this problem into two subproblems by setting (x + -0.6) equal to 1.4 and -1.4.Subproblem 1
x + -0.6 = 1.4 Simplifying x + -0.6 = 1.4 Reorder the terms: -0.6 + x = 1.4 Solving -0.6 + x = 1.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.4 + 0.6 x = 1.4 + 0.6 Combine like terms: 1.4 + 0.6 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.6 = -1.4 Simplifying x + -0.6 = -1.4 Reorder the terms: -0.6 + x = -1.4 Solving -0.6 + x = -1.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.4 + 0.6 x = -1.4 + 0.6 Combine like terms: -1.4 + 0.6 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.8}
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