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Simplifying x2 + 32x + 50 = 0 Reorder the terms: 50 + 32x + x2 = 0 Solving 50 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 32x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + 32x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 32x + x2 = 0 + -50 32x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 32x + x2 = -50 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -50 + 256 Reorder the terms: 256 + 32x + x2 = -50 + 256 Combine like terms: -50 + 256 = 206 256 + 32x + x2 = 206 Factor a perfect square on the left side: (x + 16)(x + 16) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 16) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 16 = 14.352700094 Simplifying x + 16 = 14.352700094 Reorder the terms: 16 + x = 14.352700094 Solving 16 + x = 14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 14.352700094 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.352700094 + -16 x = 14.352700094 + -16 Combine like terms: 14.352700094 + -16 = -1.647299906 x = -1.647299906 Simplifying x = -1.647299906Subproblem 2
x + 16 = -14.352700094 Simplifying x + 16 = -14.352700094 Reorder the terms: 16 + x = -14.352700094 Solving 16 + x = -14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -14.352700094 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.352700094 + -16 x = -14.352700094 + -16 Combine like terms: -14.352700094 + -16 = -30.352700094 x = -30.352700094 Simplifying x = -30.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.647299906, -30.352700094}
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