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Simplifying (x + 0.3)(x + 1.7) = 0 Reorder the terms: (0.3 + x)(x + 1.7) = 0 Reorder the terms: (0.3 + x)(1.7 + x) = 0 Multiply (0.3 + x) * (1.7 + x) (0.3(1.7 + x) + x(1.7 + x)) = 0 ((1.7 * 0.3 + x * 0.3) + x(1.7 + x)) = 0 ((0.51 + 0.3x) + x(1.7 + x)) = 0 (0.51 + 0.3x + (1.7 * x + x * x)) = 0 (0.51 + 0.3x + (1.7x + x2)) = 0 Combine like terms: 0.3x + 1.7x = 2x (0.51 + 2x + x2) = 0 Solving 0.51 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.51' to each side of the equation. 0.51 + 2x + -0.51 + x2 = 0 + -0.51 Reorder the terms: 0.51 + -0.51 + 2x + x2 = 0 + -0.51 Combine like terms: 0.51 + -0.51 = 0.00 0.00 + 2x + x2 = 0 + -0.51 2x + x2 = 0 + -0.51 Combine like terms: 0 + -0.51 = -0.51 2x + x2 = -0.51 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.51 + 1 Reorder the terms: 1 + 2x + x2 = -0.51 + 1 Combine like terms: -0.51 + 1 = 0.49 1 + 2x + x2 = 0.49 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.49 Calculate the square root of the right side: 0.7 Break this problem into two subproblems by setting (x + 1) equal to 0.7 and -0.7.Subproblem 1
x + 1 = 0.7 Simplifying x + 1 = 0.7 Reorder the terms: 1 + x = 0.7 Solving 1 + x = 0.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.7 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.7 + -1 x = 0.7 + -1 Combine like terms: 0.7 + -1 = -0.3 x = -0.3 Simplifying x = -0.3Subproblem 2
x + 1 = -0.7 Simplifying x + 1 = -0.7 Reorder the terms: 1 + x = -0.7 Solving 1 + x = -0.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.7 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.7 + -1 x = -0.7 + -1 Combine like terms: -0.7 + -1 = -1.7 x = -1.7 Simplifying x = -1.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3, -1.7}
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