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Simplifying (x + -3)(x + 6) = 10(28) Reorder the terms: (-3 + x)(x + 6) = 10(28) Reorder the terms: (-3 + x)(6 + x) = 10(28) Multiply (-3 + x) * (6 + x) (-3(6 + x) + x(6 + x)) = 10(28) ((6 * -3 + x * -3) + x(6 + x)) = 10(28) ((-18 + -3x) + x(6 + x)) = 10(28) (-18 + -3x + (6 * x + x * x)) = 10(28) (-18 + -3x + (6x + x2)) = 10(28) Combine like terms: -3x + 6x = 3x (-18 + 3x + x2) = 10(28) Multiply 10 * 28 -18 + 3x + x2 = 280 Solving -18 + 3x + x2 = 280 Solving for variable 'x'. Reorder the terms: -18 + -280 + 3x + x2 = 280 + -280 Combine like terms: -18 + -280 = -298 -298 + 3x + x2 = 280 + -280 Combine like terms: 280 + -280 = 0 -298 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '298' to each side of the equation. -298 + 3x + 298 + x2 = 0 + 298 Reorder the terms: -298 + 298 + 3x + x2 = 0 + 298 Combine like terms: -298 + 298 = 0 0 + 3x + x2 = 0 + 298 3x + x2 = 0 + 298 Combine like terms: 0 + 298 = 298 3x + x2 = 298 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 298 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 298 + 2.25 Combine like terms: 298 + 2.25 = 300.25 2.25 + 3x + x2 = 300.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (x + 1.5) equal to 17.327723451 and -17.327723451.Subproblem 1
x + 1.5 = 17.327723451 Simplifying x + 1.5 = 17.327723451 Reorder the terms: 1.5 + x = 17.327723451 Solving 1.5 + x = 17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 17.327723451 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.327723451 + -1.5 x = 17.327723451 + -1.5 Combine like terms: 17.327723451 + -1.5 = 15.827723451 x = 15.827723451 Simplifying x = 15.827723451Subproblem 2
x + 1.5 = -17.327723451 Simplifying x + 1.5 = -17.327723451 Reorder the terms: 1.5 + x = -17.327723451 Solving 1.5 + x = -17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -17.327723451 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.327723451 + -1.5 x = -17.327723451 + -1.5 Combine like terms: -17.327723451 + -1.5 = -18.827723451 x = -18.827723451 Simplifying x = -18.827723451Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.827723451, -18.827723451}
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