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Simplifying x2 + 32x + -350 = 0 Reorder the terms: -350 + 32x + x2 = 0 Solving -350 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + 32x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + 32x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + 32x + x2 = 0 + 350 32x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 32x + x2 = 350 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 = 350 + 256 Reorder the terms: 256 + 32x + x2 = 350 + 256 Combine like terms: 350 + 256 = 606 256 + 32x + x2 = 606 Factor a perfect square on the left side: (x + 16)(x + 16) = 606 Calculate the square root of the right side: 24.61706725 Break this problem into two subproblems by setting (x + 16) equal to 24.61706725 and -24.61706725.Subproblem 1
x + 16 = 24.61706725 Simplifying x + 16 = 24.61706725 Reorder the terms: 16 + x = 24.61706725 Solving 16 + x = 24.61706725 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 = 24.61706725 + -16 Combine like terms: 16 + -16 = 0 0 + x = 24.61706725 + -16 x = 24.61706725 + -16 Combine like terms: 24.61706725 + -16 = 8.61706725 x = 8.61706725 Simplifying x = 8.61706725Subproblem 2
x + 16 = -24.61706725 Simplifying x + 16 = -24.61706725 Reorder the terms: 16 + x = -24.61706725 Solving 16 + x = -24.61706725 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 = -24.61706725 + -16 Combine like terms: 16 + -16 = 0 0 + x = -24.61706725 + -16 x = -24.61706725 + -16 Combine like terms: -24.61706725 + -16 = -40.61706725 x = -40.61706725 Simplifying x = -40.61706725Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.61706725, -40.61706725}
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