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Simplifying (x + 0.3)(x + 7.5) = 0 Reorder the terms: (0.3 + x)(x + 7.5) = 0 Reorder the terms: (0.3 + x)(7.5 + x) = 0 Multiply (0.3 + x) * (7.5 + x) (0.3(7.5 + x) + x(7.5 + x)) = 0 ((7.5 * 0.3 + x * 0.3) + x(7.5 + x)) = 0 ((2.25 + 0.3x) + x(7.5 + x)) = 0 (2.25 + 0.3x + (7.5 * x + x * x)) = 0 (2.25 + 0.3x + (7.5x + x2)) = 0 Combine like terms: 0.3x + 7.5x = 7.8x (2.25 + 7.8x + x2) = 0 Solving 2.25 + 7.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 7.8x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 7.8x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 7.8x + x2 = 0 + -2.25 7.8x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 7.8x + x2 = -2.25 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -2.25 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -2.25 + 15.21 Combine like terms: -2.25 + 15.21 = 12.96 15.21 + 7.8x + x2 = 12.96 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 12.96 Calculate the square root of the right side: 3.6 Break this problem into two subproblems by setting (x + 3.9) equal to 3.6 and -3.6.Subproblem 1
x + 3.9 = 3.6 Simplifying x + 3.9 = 3.6 Reorder the terms: 3.9 + x = 3.6 Solving 3.9 + x = 3.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 3.6 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 3.6 + -3.9 x = 3.6 + -3.9 Combine like terms: 3.6 + -3.9 = -0.3 x = -0.3 Simplifying x = -0.3Subproblem 2
x + 3.9 = -3.6 Simplifying x + 3.9 = -3.6 Reorder the terms: 3.9 + x = -3.6 Solving 3.9 + x = -3.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -3.6 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -3.6 + -3.9 x = -3.6 + -3.9 Combine like terms: -3.6 + -3.9 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3, -7.5}
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