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Simplifying (2x + -0.1)(x + 2.4) = 0 Reorder the terms: (-0.1 + 2x)(x + 2.4) = 0 Reorder the terms: (-0.1 + 2x)(2.4 + x) = 0 Multiply (-0.1 + 2x) * (2.4 + x) (-0.1(2.4 + x) + 2x * (2.4 + x)) = 0 ((2.4 * -0.1 + x * -0.1) + 2x * (2.4 + x)) = 0 ((-0.24 + -0.1x) + 2x * (2.4 + x)) = 0 (-0.24 + -0.1x + (2.4 * 2x + x * 2x)) = 0 (-0.24 + -0.1x + (4.8x + 2x2)) = 0 Combine like terms: -0.1x + 4.8x = 4.7x (-0.24 + 4.7x + 2x2) = 0 Solving -0.24 + 4.7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.12 + 2.35x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + 2.35x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + 2.35x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + 2.35x + x2 = 0 + 0.12 2.35x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 2.35x + x2 = 0.12 The x term is 2.35x. Take half its coefficient (1.175). Square it (1.380625) and add it to both sides. Add '1.380625' to each side of the equation. 2.35x + 1.380625 + x2 = 0.12 + 1.380625 Reorder the terms: 1.380625 + 2.35x + x2 = 0.12 + 1.380625 Combine like terms: 0.12 + 1.380625 = 1.500625 1.380625 + 2.35x + x2 = 1.500625 Factor a perfect square on the left side: (x + 1.175)(x + 1.175) = 1.500625 Calculate the square root of the right side: 1.225 Break this problem into two subproblems by setting (x + 1.175) equal to 1.225 and -1.225.Subproblem 1
x + 1.175 = 1.225 Simplifying x + 1.175 = 1.225 Reorder the terms: 1.175 + x = 1.225 Solving 1.175 + x = 1.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = 1.225 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = 1.225 + -1.175 x = 1.225 + -1.175 Combine like terms: 1.225 + -1.175 = 0.05 x = 0.05 Simplifying x = 0.05Subproblem 2
x + 1.175 = -1.225 Simplifying x + 1.175 = -1.225 Reorder the terms: 1.175 + x = -1.225 Solving 1.175 + x = -1.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = -1.225 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = -1.225 + -1.175 x = -1.225 + -1.175 Combine like terms: -1.225 + -1.175 = -2.4 x = -2.4 Simplifying x = -2.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.05, -2.4}
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