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Simplifying (x + 14)(x + 14) = 1236 Reorder the terms: (14 + x)(x + 14) = 1236 Reorder the terms: (14 + x)(14 + x) = 1236 Multiply (14 + x) * (14 + x) (14(14 + x) + x(14 + x)) = 1236 ((14 * 14 + x * 14) + x(14 + x)) = 1236 ((196 + 14x) + x(14 + x)) = 1236 (196 + 14x + (14 * x + x * x)) = 1236 (196 + 14x + (14x + x2)) = 1236 Combine like terms: 14x + 14x = 28x (196 + 28x + x2) = 1236 Solving 196 + 28x + x2 = 1236 Solving for variable 'x'. Reorder the terms: 196 + -1236 + 28x + x2 = 1236 + -1236 Combine like terms: 196 + -1236 = -1040 -1040 + 28x + x2 = 1236 + -1236 Combine like terms: 1236 + -1236 = 0 -1040 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1040' to each side of the equation. -1040 + 28x + 1040 + x2 = 0 + 1040 Reorder the terms: -1040 + 1040 + 28x + x2 = 0 + 1040 Combine like terms: -1040 + 1040 = 0 0 + 28x + x2 = 0 + 1040 28x + x2 = 0 + 1040 Combine like terms: 0 + 1040 = 1040 28x + x2 = 1040 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 1040 + 196 Reorder the terms: 196 + 28x + x2 = 1040 + 196 Combine like terms: 1040 + 196 = 1236 196 + 28x + x2 = 1236 Factor a perfect square on the left side: (x + 14)(x + 14) = 1236 Calculate the square root of the right side: 35.156791662 Break this problem into two subproblems by setting (x + 14) equal to 35.156791662 and -35.156791662.Subproblem 1
x + 14 = 35.156791662 Simplifying x + 14 = 35.156791662 Reorder the terms: 14 + x = 35.156791662 Solving 14 + x = 35.156791662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 35.156791662 + -14 Combine like terms: 14 + -14 = 0 0 + x = 35.156791662 + -14 x = 35.156791662 + -14 Combine like terms: 35.156791662 + -14 = 21.156791662 x = 21.156791662 Simplifying x = 21.156791662Subproblem 2
x + 14 = -35.156791662 Simplifying x + 14 = -35.156791662 Reorder the terms: 14 + x = -35.156791662 Solving 14 + x = -35.156791662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -35.156791662 + -14 Combine like terms: 14 + -14 = 0 0 + x = -35.156791662 + -14 x = -35.156791662 + -14 Combine like terms: -35.156791662 + -14 = -49.156791662 x = -49.156791662 Simplifying x = -49.156791662Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.156791662, -49.156791662}
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