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Simplifying 0.015625x2 + -1x + 12 = 0 Reorder the terms: 12 + -1x + 0.015625x2 = 0 Solving 12 + -1x + 0.015625x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.015625 the coefficient of the squared term: Divide each side by '0.015625'. 768 + -64x + x2 = 0 Move the constant term to the right: Add '-768' to each side of the equation. 768 + -64x + -768 + x2 = 0 + -768 Reorder the terms: 768 + -768 + -64x + x2 = 0 + -768 Combine like terms: 768 + -768 = 0 0 + -64x + x2 = 0 + -768 -64x + x2 = 0 + -768 Combine like terms: 0 + -768 = -768 -64x + x2 = -768 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = -768 + 1024 Reorder the terms: 1024 + -64x + x2 = -768 + 1024 Combine like terms: -768 + 1024 = 256 1024 + -64x + x2 = 256 Factor a perfect square on the left side: (x + -32)(x + -32) = 256 Calculate the square root of the right side: 16 Break this problem into two subproblems by setting (x + -32) equal to 16 and -16.Subproblem 1
x + -32 = 16 Simplifying x + -32 = 16 Reorder the terms: -32 + x = 16 Solving -32 + x = 16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 16 + 32 Combine like terms: -32 + 32 = 0 0 + x = 16 + 32 x = 16 + 32 Combine like terms: 16 + 32 = 48 x = 48 Simplifying x = 48Subproblem 2
x + -32 = -16 Simplifying x + -32 = -16 Reorder the terms: -32 + x = -16 Solving -32 + x = -16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -16 + 32 Combine like terms: -32 + 32 = 0 0 + x = -16 + 32 x = -16 + 32 Combine like terms: -16 + 32 = 16 x = 16 Simplifying x = 16Solution
The solution to the problem is based on the solutions from the subproblems. x = {48, 16}
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