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Simplifying 3x + 34x + -10 = -1x2 + -40 Reorder the terms: -10 + 3x + 34x = -1x2 + -40 Combine like terms: 3x + 34x = 37x -10 + 37x = -1x2 + -40 Reorder the terms: -10 + 37x = -40 + -1x2 Solving -10 + 37x = -40 + -1x2 Solving for variable 'x'. Reorder the terms: -10 + 40 + 37x + x2 = -40 + -1x2 + 40 + x2 Combine like terms: -10 + 40 = 30 30 + 37x + x2 = -40 + -1x2 + 40 + x2 Reorder the terms: 30 + 37x + x2 = -40 + 40 + -1x2 + x2 Combine like terms: -40 + 40 = 0 30 + 37x + x2 = 0 + -1x2 + x2 30 + 37x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 30 + 37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 37x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 37x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 37x + x2 = 0 + -30 37x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 37x + x2 = -30 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -30 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -30 + 342.25 Combine like terms: -30 + 342.25 = 312.25 342.25 + 37x + x2 = 312.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (x + 18.5) equal to 17.670597047 and -17.670597047.Subproblem 1
x + 18.5 = 17.670597047 Simplifying x + 18.5 = 17.670597047 Reorder the terms: 18.5 + x = 17.670597047 Solving 18.5 + x = 17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 17.670597047 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.670597047 + -18.5 x = 17.670597047 + -18.5 Combine like terms: 17.670597047 + -18.5 = -0.829402953 x = -0.829402953 Simplifying x = -0.829402953Subproblem 2
x + 18.5 = -17.670597047 Simplifying x + 18.5 = -17.670597047 Reorder the terms: 18.5 + x = -17.670597047 Solving 18.5 + x = -17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -17.670597047 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.670597047 + -18.5 x = -17.670597047 + -18.5 Combine like terms: -17.670597047 + -18.5 = -36.170597047 x = -36.170597047 Simplifying x = -36.170597047Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.829402953, -36.170597047}
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