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Simplifying (x + -0.3)(x + 0.5) = 0 Reorder the terms: (-0.3 + x)(x + 0.5) = 0 Reorder the terms: (-0.3 + x)(0.5 + x) = 0 Multiply (-0.3 + x) * (0.5 + x) (-0.3(0.5 + x) + x(0.5 + x)) = 0 ((0.5 * -0.3 + x * -0.3) + x(0.5 + x)) = 0 ((-0.15 + -0.3x) + x(0.5 + x)) = 0 (-0.15 + -0.3x + (0.5 * x + x * x)) = 0 (-0.15 + -0.3x + (0.5x + x2)) = 0 Combine like terms: -0.3x + 0.5x = 0.2x (-0.15 + 0.2x + x2) = 0 Solving -0.15 + 0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 0.2x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + 0.2x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 0.2x + x2 = 0 + 0.15 0.2x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 0.2x + x2 = 0.15 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.15 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.15 + 0.01 Combine like terms: 0.15 + 0.01 = 0.16 0.01 + 0.2x + x2 = 0.16 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + 0.1) equal to 0.4 and -0.4.Subproblem 1
x + 0.1 = 0.4 Simplifying x + 0.1 = 0.4 Reorder the terms: 0.1 + x = 0.4 Solving 0.1 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.4 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.4 + -0.1 x = 0.4 + -0.1 Combine like terms: 0.4 + -0.1 = 0.3 x = 0.3 Simplifying x = 0.3Subproblem 2
x + 0.1 = -0.4 Simplifying x + 0.1 = -0.4 Reorder the terms: 0.1 + x = -0.4 Solving 0.1 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.4 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.4 + -0.1 x = -0.4 + -0.1 Combine like terms: -0.4 + -0.1 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3, -0.5}
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