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Simplifying 16 + -16x + -1x2 = 4x + 5 Reorder the terms: 16 + -16x + -1x2 = 5 + 4x Solving 16 + -16x + -1x2 = 5 + 4x Solving for variable 'x'. Reorder the terms: 16 + -5 + -16x + -4x + -1x2 = 5 + 4x + -5 + -4x Combine like terms: 16 + -5 = 11 11 + -16x + -4x + -1x2 = 5 + 4x + -5 + -4x Combine like terms: -16x + -4x = -20x 11 + -20x + -1x2 = 5 + 4x + -5 + -4x Reorder the terms: 11 + -20x + -1x2 = 5 + -5 + 4x + -4x Combine like terms: 5 + -5 = 0 11 + -20x + -1x2 = 0 + 4x + -4x 11 + -20x + -1x2 = 4x + -4x Combine like terms: 4x + -4x = 0 11 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 20x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 20x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 20x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 20x + x2 = 0 + 11 20x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 20x + x2 = 11 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 11 + 100 Reorder the terms: 100 + 20x + x2 = 11 + 100 Combine like terms: 11 + 100 = 111 100 + 20x + x2 = 111 Factor a perfect square on the left side: (x + 10)(x + 10) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + 10) equal to 10.535653753 and -10.535653753.Subproblem 1
x + 10 = 10.535653753 Simplifying x + 10 = 10.535653753 Reorder the terms: 10 + x = 10.535653753 Solving 10 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.535653753 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.535653753 + -10 x = 10.535653753 + -10 Combine like terms: 10.535653753 + -10 = 0.535653753 x = 0.535653753 Simplifying x = 0.535653753Subproblem 2
x + 10 = -10.535653753 Simplifying x + 10 = -10.535653753 Reorder the terms: 10 + x = -10.535653753 Solving 10 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.535653753 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.535653753 + -10 x = -10.535653753 + -10 Combine like terms: -10.535653753 + -10 = -20.535653753 x = -20.535653753 Simplifying x = -20.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.535653753, -20.535653753}
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