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Simplifying 0 = x2 + 32x + -192 Reorder the terms: 0 = -192 + 32x + x2 Solving 0 = -192 + 32x + x2 Solving for variable 'x'. Combine like terms: 0 + 192 = 192 192 + -32x + -1x2 = -192 + 32x + x2 + 192 + -32x + -1x2 Reorder the terms: 192 + -32x + -1x2 = -192 + 192 + 32x + -32x + x2 + -1x2 Combine like terms: -192 + 192 = 0 192 + -32x + -1x2 = 0 + 32x + -32x + x2 + -1x2 192 + -32x + -1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 192 + -32x + -1x2 = 0 + x2 + -1x2 192 + -32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 192 + -32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -192 + 32x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 32x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 32x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 32x + x2 = 0 + 192 32x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 32x + x2 = 192 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 = 192 + 256 Reorder the terms: 256 + 32x + x2 = 192 + 256 Combine like terms: 192 + 256 = 448 256 + 32x + x2 = 448 Factor a perfect square on the left side: (x + 16)(x + 16) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 16) equal to 21.166010489 and -21.166010489.Subproblem 1
x + 16 = 21.166010489 Simplifying x + 16 = 21.166010489 Reorder the terms: 16 + x = 21.166010489 Solving 16 + x = 21.166010489 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 = 21.166010489 + -16 Combine like terms: 16 + -16 = 0 0 + x = 21.166010489 + -16 x = 21.166010489 + -16 Combine like terms: 21.166010489 + -16 = 5.166010489 x = 5.166010489 Simplifying x = 5.166010489Subproblem 2
x + 16 = -21.166010489 Simplifying x + 16 = -21.166010489 Reorder the terms: 16 + x = -21.166010489 Solving 16 + x = -21.166010489 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 = -21.166010489 + -16 Combine like terms: 16 + -16 = 0 0 + x = -21.166010489 + -16 x = -21.166010489 + -16 Combine like terms: -21.166010489 + -16 = -37.166010489 x = -37.166010489 Simplifying x = -37.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.166010489, -37.166010489}
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