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Simplifying 0 = -16x2 + 96x + 233 Reorder the terms: 0 = 233 + 96x + -16x2 Solving 0 = 233 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -233 = -233 -233 + -96x + 16x2 = 233 + 96x + -16x2 + -233 + -96x + 16x2 Reorder the terms: -233 + -96x + 16x2 = 233 + -233 + 96x + -96x + -16x2 + 16x2 Combine like terms: 233 + -233 = 0 -233 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -233 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -233 + -96x + 16x2 = 0 + -16x2 + 16x2 -233 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -233 + -96x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -14.5625 + -6x + x2 = 0 Move the constant term to the right: Add '14.5625' to each side of the equation. -14.5625 + -6x + 14.5625 + x2 = 0 + 14.5625 Reorder the terms: -14.5625 + 14.5625 + -6x + x2 = 0 + 14.5625 Combine like terms: -14.5625 + 14.5625 = 0.0000 0.0000 + -6x + x2 = 0 + 14.5625 -6x + x2 = 0 + 14.5625 Combine like terms: 0 + 14.5625 = 14.5625 -6x + x2 = 14.5625 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 14.5625 + 9 Reorder the terms: 9 + -6x + x2 = 14.5625 + 9 Combine like terms: 14.5625 + 9 = 23.5625 9 + -6x + x2 = 23.5625 Factor a perfect square on the left side: (x + -3)(x + -3) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (x + -3) equal to 4.85412196 and -4.85412196.Subproblem 1
x + -3 = 4.85412196 Simplifying x + -3 = 4.85412196 Reorder the terms: -3 + x = 4.85412196 Solving -3 + x = 4.85412196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.85412196 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.85412196 + 3 x = 4.85412196 + 3 Combine like terms: 4.85412196 + 3 = 7.85412196 x = 7.85412196 Simplifying x = 7.85412196Subproblem 2
x + -3 = -4.85412196 Simplifying x + -3 = -4.85412196 Reorder the terms: -3 + x = -4.85412196 Solving -3 + x = -4.85412196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.85412196 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.85412196 + 3 x = -4.85412196 + 3 Combine like terms: -4.85412196 + 3 = -1.85412196 x = -1.85412196 Simplifying x = -1.85412196Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.85412196, -1.85412196}
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