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Simplifying x2 + 14x = 236 Reorder the terms: 14x + x2 = 236 Solving 14x + x2 = 236 Solving for variable 'x'. Reorder the terms: -236 + 14x + x2 = 236 + -236 Combine like terms: 236 + -236 = 0 -236 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '236' to each side of the equation. -236 + 14x + 236 + x2 = 0 + 236 Reorder the terms: -236 + 236 + 14x + x2 = 0 + 236 Combine like terms: -236 + 236 = 0 0 + 14x + x2 = 0 + 236 14x + x2 = 0 + 236 Combine like terms: 0 + 236 = 236 14x + x2 = 236 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 236 + 49 Reorder the terms: 49 + 14x + x2 = 236 + 49 Combine like terms: 236 + 49 = 285 49 + 14x + x2 = 285 Factor a perfect square on the left side: (x + 7)(x + 7) = 285 Calculate the square root of the right side: 16.881943016 Break this problem into two subproblems by setting (x + 7) equal to 16.881943016 and -16.881943016.Subproblem 1
x + 7 = 16.881943016 Simplifying x + 7 = 16.881943016 Reorder the terms: 7 + x = 16.881943016 Solving 7 + x = 16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 16.881943016 + -7 Combine like terms: 7 + -7 = 0 0 + x = 16.881943016 + -7 x = 16.881943016 + -7 Combine like terms: 16.881943016 + -7 = 9.881943016 x = 9.881943016 Simplifying x = 9.881943016Subproblem 2
x + 7 = -16.881943016 Simplifying x + 7 = -16.881943016 Reorder the terms: 7 + x = -16.881943016 Solving 7 + x = -16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -16.881943016 + -7 Combine like terms: 7 + -7 = 0 0 + x = -16.881943016 + -7 x = -16.881943016 + -7 Combine like terms: -16.881943016 + -7 = -23.881943016 x = -23.881943016 Simplifying x = -23.881943016Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.881943016, -23.881943016}
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