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Simplifying 18x + x2 = 30 Solving 18x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 18x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 18x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 18x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 18x + x2 = 0 + 30 18x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 18x + x2 = 30 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 30 + 81 Reorder the terms: 81 + 18x + x2 = 30 + 81 Combine like terms: 30 + 81 = 111 81 + 18x + x2 = 111 Factor a perfect square on the left side: (x + 9)(x + 9) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + 9) equal to 10.535653753 and -10.535653753.Subproblem 1
x + 9 = 10.535653753 Simplifying x + 9 = 10.535653753 Reorder the terms: 9 + x = 10.535653753 Solving 9 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 10.535653753 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.535653753 + -9 x = 10.535653753 + -9 Combine like terms: 10.535653753 + -9 = 1.535653753 x = 1.535653753 Simplifying x = 1.535653753Subproblem 2
x + 9 = -10.535653753 Simplifying x + 9 = -10.535653753 Reorder the terms: 9 + x = -10.535653753 Solving 9 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -10.535653753 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.535653753 + -9 x = -10.535653753 + -9 Combine like terms: -10.535653753 + -9 = -19.535653753 x = -19.535653753 Simplifying x = -19.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.535653753, -19.535653753}
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