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Simplifying 46x + x2 = 1224 Solving 46x + x2 = 1224 Solving for variable 'x'. Reorder the terms: -1224 + 46x + x2 = 1224 + -1224 Combine like terms: 1224 + -1224 = 0 -1224 + 46x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1224' to each side of the equation. -1224 + 46x + 1224 + x2 = 0 + 1224 Reorder the terms: -1224 + 1224 + 46x + x2 = 0 + 1224 Combine like terms: -1224 + 1224 = 0 0 + 46x + x2 = 0 + 1224 46x + x2 = 0 + 1224 Combine like terms: 0 + 1224 = 1224 46x + x2 = 1224 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 1224 + 529 Reorder the terms: 529 + 46x + x2 = 1224 + 529 Combine like terms: 1224 + 529 = 1753 529 + 46x + x2 = 1753 Factor a perfect square on the left side: (x + 23)(x + 23) = 1753 Calculate the square root of the right side: 41.868842831 Break this problem into two subproblems by setting (x + 23) equal to 41.868842831 and -41.868842831.Subproblem 1
x + 23 = 41.868842831 Simplifying x + 23 = 41.868842831 Reorder the terms: 23 + x = 41.868842831 Solving 23 + x = 41.868842831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 41.868842831 + -23 Combine like terms: 23 + -23 = 0 0 + x = 41.868842831 + -23 x = 41.868842831 + -23 Combine like terms: 41.868842831 + -23 = 18.868842831 x = 18.868842831 Simplifying x = 18.868842831Subproblem 2
x + 23 = -41.868842831 Simplifying x + 23 = -41.868842831 Reorder the terms: 23 + x = -41.868842831 Solving 23 + x = -41.868842831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -41.868842831 + -23 Combine like terms: 23 + -23 = 0 0 + x = -41.868842831 + -23 x = -41.868842831 + -23 Combine like terms: -41.868842831 + -23 = -64.868842831 x = -64.868842831 Simplifying x = -64.868842831Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.868842831, -64.868842831}
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