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Simplifying 6.28x2 + 8x = 60 Reorder the terms: 8x + 6.28x2 = 60 Solving 8x + 6.28x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 8x + 6.28x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 8x + 6.28x2 = 0 Begin completing the square. Divide all terms by 6.28 the coefficient of the squared term: Divide each side by '6.28'. -9.554140127 + 1.27388535x + x2 = 0 Move the constant term to the right: Add '9.554140127' to each side of the equation. -9.554140127 + 1.27388535x + 9.554140127 + x2 = 0 + 9.554140127 Reorder the terms: -9.554140127 + 9.554140127 + 1.27388535x + x2 = 0 + 9.554140127 Combine like terms: -9.554140127 + 9.554140127 = 0.000000000 0.000000000 + 1.27388535x + x2 = 0 + 9.554140127 1.27388535x + x2 = 0 + 9.554140127 Combine like terms: 0 + 9.554140127 = 9.554140127 1.27388535x + x2 = 9.554140127 The x term is 1.27388535x. Take half its coefficient (0.636942675). Square it (0.4056959712) and add it to both sides. Add '0.4056959712' to each side of the equation. 1.27388535x + 0.4056959712 + x2 = 9.554140127 + 0.4056959712 Reorder the terms: 0.4056959712 + 1.27388535x + x2 = 9.554140127 + 0.4056959712 Combine like terms: 9.554140127 + 0.4056959712 = 9.9598360982 0.4056959712 + 1.27388535x + x2 = 9.9598360982 Factor a perfect square on the left side: (x + 0.636942675)(x + 0.636942675) = 9.9598360982 Calculate the square root of the right side: 3.1559208 Break this problem into two subproblems by setting (x + 0.636942675) equal to 3.1559208 and -3.1559208.Subproblem 1
x + 0.636942675 = 3.1559208 Simplifying x + 0.636942675 = 3.1559208 Reorder the terms: 0.636942675 + x = 3.1559208 Solving 0.636942675 + x = 3.1559208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.636942675' to each side of the equation. 0.636942675 + -0.636942675 + x = 3.1559208 + -0.636942675 Combine like terms: 0.636942675 + -0.636942675 = 0.000000000 0.000000000 + x = 3.1559208 + -0.636942675 x = 3.1559208 + -0.636942675 Combine like terms: 3.1559208 + -0.636942675 = 2.518978125 x = 2.518978125 Simplifying x = 2.518978125Subproblem 2
x + 0.636942675 = -3.1559208 Simplifying x + 0.636942675 = -3.1559208 Reorder the terms: 0.636942675 + x = -3.1559208 Solving 0.636942675 + x = -3.1559208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.636942675' to each side of the equation. 0.636942675 + -0.636942675 + x = -3.1559208 + -0.636942675 Combine like terms: 0.636942675 + -0.636942675 = 0.000000000 0.000000000 + x = -3.1559208 + -0.636942675 x = -3.1559208 + -0.636942675 Combine like terms: -3.1559208 + -0.636942675 = -3.792863475 x = -3.792863475 Simplifying x = -3.792863475Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.518978125, -3.792863475}
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