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Simplifying 96 + -28x = x2 Solving 96 + -28x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 96 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 28x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 28x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 28x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 28x + x2 = 0 + 96 28x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 28x + x2 = 96 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 96 + 196 Reorder the terms: 196 + 28x + x2 = 96 + 196 Combine like terms: 96 + 196 = 292 196 + 28x + x2 = 292 Factor a perfect square on the left side: (x + 14)(x + 14) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + 14) equal to 17.088007491 and -17.088007491.Subproblem 1
x + 14 = 17.088007491 Simplifying x + 14 = 17.088007491 Reorder the terms: 14 + x = 17.088007491 Solving 14 + x = 17.088007491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 17.088007491 + -14 Combine like terms: 14 + -14 = 0 0 + x = 17.088007491 + -14 x = 17.088007491 + -14 Combine like terms: 17.088007491 + -14 = 3.088007491 x = 3.088007491 Simplifying x = 3.088007491Subproblem 2
x + 14 = -17.088007491 Simplifying x + 14 = -17.088007491 Reorder the terms: 14 + x = -17.088007491 Solving 14 + x = -17.088007491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -17.088007491 + -14 Combine like terms: 14 + -14 = 0 0 + x = -17.088007491 + -14 x = -17.088007491 + -14 Combine like terms: -17.088007491 + -14 = -31.088007491 x = -31.088007491 Simplifying x = -31.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.088007491, -31.088007491}
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