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Simplifying x2 + 8x + 12 = 35x + 1505 Reorder the terms: 12 + 8x + x2 = 35x + 1505 Reorder the terms: 12 + 8x + x2 = 1505 + 35x Solving 12 + 8x + x2 = 1505 + 35x Solving for variable 'x'. Reorder the terms: 12 + -1505 + 8x + -35x + x2 = 1505 + 35x + -1505 + -35x Combine like terms: 12 + -1505 = -1493 -1493 + 8x + -35x + x2 = 1505 + 35x + -1505 + -35x Combine like terms: 8x + -35x = -27x -1493 + -27x + x2 = 1505 + 35x + -1505 + -35x Reorder the terms: -1493 + -27x + x2 = 1505 + -1505 + 35x + -35x Combine like terms: 1505 + -1505 = 0 -1493 + -27x + x2 = 0 + 35x + -35x -1493 + -27x + x2 = 35x + -35x Combine like terms: 35x + -35x = 0 -1493 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1493' to each side of the equation. -1493 + -27x + 1493 + x2 = 0 + 1493 Reorder the terms: -1493 + 1493 + -27x + x2 = 0 + 1493 Combine like terms: -1493 + 1493 = 0 0 + -27x + x2 = 0 + 1493 -27x + x2 = 0 + 1493 Combine like terms: 0 + 1493 = 1493 -27x + x2 = 1493 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = 1493 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 1493 + 182.25 Combine like terms: 1493 + 182.25 = 1675.25 182.25 + -27x + x2 = 1675.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 1675.25 Calculate the square root of the right side: 40.929817982 Break this problem into two subproblems by setting (x + -13.5) equal to 40.929817982 and -40.929817982.Subproblem 1
x + -13.5 = 40.929817982 Simplifying x + -13.5 = 40.929817982 Reorder the terms: -13.5 + x = 40.929817982 Solving -13.5 + x = 40.929817982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 40.929817982 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 40.929817982 + 13.5 x = 40.929817982 + 13.5 Combine like terms: 40.929817982 + 13.5 = 54.429817982 x = 54.429817982 Simplifying x = 54.429817982Subproblem 2
x + -13.5 = -40.929817982 Simplifying x + -13.5 = -40.929817982 Reorder the terms: -13.5 + x = -40.929817982 Solving -13.5 + x = -40.929817982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -40.929817982 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -40.929817982 + 13.5 x = -40.929817982 + 13.5 Combine like terms: -40.929817982 + 13.5 = -27.429817982 x = -27.429817982 Simplifying x = -27.429817982Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.429817982, -27.429817982}
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