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Simplifying (x + -4)(x + 1) = 54 Reorder the terms: (-4 + x)(x + 1) = 54 Reorder the terms: (-4 + x)(1 + x) = 54 Multiply (-4 + x) * (1 + x) (-4(1 + x) + x(1 + x)) = 54 ((1 * -4 + x * -4) + x(1 + x)) = 54 ((-4 + -4x) + x(1 + x)) = 54 (-4 + -4x + (1 * x + x * x)) = 54 (-4 + -4x + (1x + x2)) = 54 Combine like terms: -4x + 1x = -3x (-4 + -3x + x2) = 54 Solving -4 + -3x + x2 = 54 Solving for variable 'x'. Reorder the terms: -4 + -54 + -3x + x2 = 54 + -54 Combine like terms: -4 + -54 = -58 -58 + -3x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -58 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -3x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + -3x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -3x + x2 = 0 + 58 -3x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 -3x + x2 = 58 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 = 58 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 58 + 2.25 Combine like terms: 58 + 2.25 = 60.25 2.25 + -3x + x2 = 60.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -1.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -1.5 = 7.762087348 Simplifying x + -1.5 = 7.762087348 Reorder the terms: -1.5 + x = 7.762087348 Solving -1.5 + x = 7.762087348 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 = 7.762087348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.762087348 + 1.5 x = 7.762087348 + 1.5 Combine like terms: 7.762087348 + 1.5 = 9.262087348 x = 9.262087348 Simplifying x = 9.262087348Subproblem 2
x + -1.5 = -7.762087348 Simplifying x + -1.5 = -7.762087348 Reorder the terms: -1.5 + x = -7.762087348 Solving -1.5 + x = -7.762087348 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 = -7.762087348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.762087348 + 1.5 x = -7.762087348 + 1.5 Combine like terms: -7.762087348 + 1.5 = -6.262087348 x = -6.262087348 Simplifying x = -6.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.262087348, -6.262087348}
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