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Simplifying x2 + 8x + 12 = 5x + 25 Reorder the terms: 12 + 8x + x2 = 5x + 25 Reorder the terms: 12 + 8x + x2 = 25 + 5x Solving 12 + 8x + x2 = 25 + 5x Solving for variable 'x'. Reorder the terms: 12 + -25 + 8x + -5x + x2 = 25 + 5x + -25 + -5x Combine like terms: 12 + -25 = -13 -13 + 8x + -5x + x2 = 25 + 5x + -25 + -5x Combine like terms: 8x + -5x = 3x -13 + 3x + x2 = 25 + 5x + -25 + -5x Reorder the terms: -13 + 3x + x2 = 25 + -25 + 5x + -5x Combine like terms: 25 + -25 = 0 -13 + 3x + x2 = 0 + 5x + -5x -13 + 3x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -13 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 3x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 3x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3x + x2 = 0 + 13 3x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 3x + x2 = 13 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 = 13 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + 3x + x2 = 15.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 1.5 = 3.905124838 Simplifying x + 1.5 = 3.905124838 Reorder the terms: 1.5 + x = 3.905124838 Solving 1.5 + x = 3.905124838 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 = 3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.905124838 + -1.5 x = 3.905124838 + -1.5 Combine like terms: 3.905124838 + -1.5 = 2.405124838 x = 2.405124838 Simplifying x = 2.405124838Subproblem 2
x + 1.5 = -3.905124838 Simplifying x + 1.5 = -3.905124838 Reorder the terms: 1.5 + x = -3.905124838 Solving 1.5 + x = -3.905124838 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 = -3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.905124838 + -1.5 x = -3.905124838 + -1.5 Combine like terms: -3.905124838 + -1.5 = -5.405124838 x = -5.405124838 Simplifying x = -5.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.405124838, -5.405124838}
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