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Simplifying 112 + -32x + -1x2 = 0 Solving 112 + -32x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -112 + 32x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + 32x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 32x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 32x + x2 = 0 + 112 32x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 32x + x2 = 112 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 = 112 + 256 Reorder the terms: 256 + 32x + x2 = 112 + 256 Combine like terms: 112 + 256 = 368 256 + 32x + x2 = 368 Factor a perfect square on the left side: (x + 16)(x + 16) = 368 Calculate the square root of the right side: 19.183326093 Break this problem into two subproblems by setting (x + 16) equal to 19.183326093 and -19.183326093.Subproblem 1
x + 16 = 19.183326093 Simplifying x + 16 = 19.183326093 Reorder the terms: 16 + x = 19.183326093 Solving 16 + x = 19.183326093 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 = 19.183326093 + -16 Combine like terms: 16 + -16 = 0 0 + x = 19.183326093 + -16 x = 19.183326093 + -16 Combine like terms: 19.183326093 + -16 = 3.183326093 x = 3.183326093 Simplifying x = 3.183326093Subproblem 2
x + 16 = -19.183326093 Simplifying x + 16 = -19.183326093 Reorder the terms: 16 + x = -19.183326093 Solving 16 + x = -19.183326093 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 = -19.183326093 + -16 Combine like terms: 16 + -16 = 0 0 + x = -19.183326093 + -16 x = -19.183326093 + -16 Combine like terms: -19.183326093 + -16 = -35.183326093 x = -35.183326093 Simplifying x = -35.183326093Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.183326093, -35.183326093}
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