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Simplifying (x + 4)(x + 14) = 900 Reorder the terms: (4 + x)(x + 14) = 900 Reorder the terms: (4 + x)(14 + x) = 900 Multiply (4 + x) * (14 + x) (4(14 + x) + x(14 + x)) = 900 ((14 * 4 + x * 4) + x(14 + x)) = 900 ((56 + 4x) + x(14 + x)) = 900 (56 + 4x + (14 * x + x * x)) = 900 (56 + 4x + (14x + x2)) = 900 Combine like terms: 4x + 14x = 18x (56 + 18x + x2) = 900 Solving 56 + 18x + x2 = 900 Solving for variable 'x'. Reorder the terms: 56 + -900 + 18x + x2 = 900 + -900 Combine like terms: 56 + -900 = -844 -844 + 18x + x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -844 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '844' to each side of the equation. -844 + 18x + 844 + x2 = 0 + 844 Reorder the terms: -844 + 844 + 18x + x2 = 0 + 844 Combine like terms: -844 + 844 = 0 0 + 18x + x2 = 0 + 844 18x + x2 = 0 + 844 Combine like terms: 0 + 844 = 844 18x + x2 = 844 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 = 844 + 81 Reorder the terms: 81 + 18x + x2 = 844 + 81 Combine like terms: 844 + 81 = 925 81 + 18x + x2 = 925 Factor a perfect square on the left side: (x + 9)(x + 9) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (x + 9) equal to 30.413812651 and -30.413812651.Subproblem 1
x + 9 = 30.413812651 Simplifying x + 9 = 30.413812651 Reorder the terms: 9 + x = 30.413812651 Solving 9 + x = 30.413812651 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 = 30.413812651 + -9 Combine like terms: 9 + -9 = 0 0 + x = 30.413812651 + -9 x = 30.413812651 + -9 Combine like terms: 30.413812651 + -9 = 21.413812651 x = 21.413812651 Simplifying x = 21.413812651Subproblem 2
x + 9 = -30.413812651 Simplifying x + 9 = -30.413812651 Reorder the terms: 9 + x = -30.413812651 Solving 9 + x = -30.413812651 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 = -30.413812651 + -9 Combine like terms: 9 + -9 = 0 0 + x = -30.413812651 + -9 x = -30.413812651 + -9 Combine like terms: -30.413812651 + -9 = -39.413812651 x = -39.413812651 Simplifying x = -39.413812651Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.413812651, -39.413812651}
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