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Simplifying 16x2 + 24x + 16 = 81 Reorder the terms: 16 + 24x + 16x2 = 81 Solving 16 + 24x + 16x2 = 81 Solving for variable 'x'. Reorder the terms: 16 + -81 + 24x + 16x2 = 81 + -81 Combine like terms: 16 + -81 = -65 -65 + 24x + 16x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -65 + 24x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.0625 + 1.5x + x2 = 0 Move the constant term to the right: Add '4.0625' to each side of the equation. -4.0625 + 1.5x + 4.0625 + x2 = 0 + 4.0625 Reorder the terms: -4.0625 + 4.0625 + 1.5x + x2 = 0 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + 1.5x + x2 = 0 + 4.0625 1.5x + x2 = 0 + 4.0625 Combine like terms: 0 + 4.0625 = 4.0625 1.5x + x2 = 4.0625 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 4.0625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 4.0625 + 0.5625 Combine like terms: 4.0625 + 0.5625 = 4.625 0.5625 + 1.5x + x2 = 4.625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.625 Calculate the square root of the right side: 2.150581317 Break this problem into two subproblems by setting (x + 0.75) equal to 2.150581317 and -2.150581317.Subproblem 1
x + 0.75 = 2.150581317 Simplifying x + 0.75 = 2.150581317 Reorder the terms: 0.75 + x = 2.150581317 Solving 0.75 + x = 2.150581317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.150581317 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.150581317 + -0.75 x = 2.150581317 + -0.75 Combine like terms: 2.150581317 + -0.75 = 1.400581317 x = 1.400581317 Simplifying x = 1.400581317Subproblem 2
x + 0.75 = -2.150581317 Simplifying x + 0.75 = -2.150581317 Reorder the terms: 0.75 + x = -2.150581317 Solving 0.75 + x = -2.150581317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.150581317 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.150581317 + -0.75 x = -2.150581317 + -0.75 Combine like terms: -2.150581317 + -0.75 = -2.900581317 x = -2.900581317 Simplifying x = -2.900581317Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.400581317, -2.900581317}
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