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Simplifying x2 + 10x + 4x + 21 = 360 Reorder the terms: 21 + 10x + 4x + x2 = 360 Combine like terms: 10x + 4x = 14x 21 + 14x + x2 = 360 Solving 21 + 14x + x2 = 360 Solving for variable 'x'. Reorder the terms: 21 + -360 + 14x + x2 = 360 + -360 Combine like terms: 21 + -360 = -339 -339 + 14x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -339 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '339' to each side of the equation. -339 + 14x + 339 + x2 = 0 + 339 Reorder the terms: -339 + 339 + 14x + x2 = 0 + 339 Combine like terms: -339 + 339 = 0 0 + 14x + x2 = 0 + 339 14x + x2 = 0 + 339 Combine like terms: 0 + 339 = 339 14x + x2 = 339 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 = 339 + 49 Reorder the terms: 49 + 14x + x2 = 339 + 49 Combine like terms: 339 + 49 = 388 49 + 14x + x2 = 388 Factor a perfect square on the left side: (x + 7)(x + 7) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (x + 7) equal to 19.697715604 and -19.697715604.Subproblem 1
x + 7 = 19.697715604 Simplifying x + 7 = 19.697715604 Reorder the terms: 7 + x = 19.697715604 Solving 7 + x = 19.697715604 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 = 19.697715604 + -7 Combine like terms: 7 + -7 = 0 0 + x = 19.697715604 + -7 x = 19.697715604 + -7 Combine like terms: 19.697715604 + -7 = 12.697715604 x = 12.697715604 Simplifying x = 12.697715604Subproblem 2
x + 7 = -19.697715604 Simplifying x + 7 = -19.697715604 Reorder the terms: 7 + x = -19.697715604 Solving 7 + x = -19.697715604 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 = -19.697715604 + -7 Combine like terms: 7 + -7 = 0 0 + x = -19.697715604 + -7 x = -19.697715604 + -7 Combine like terms: -19.697715604 + -7 = -26.697715604 x = -26.697715604 Simplifying x = -26.697715604Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.697715604, -26.697715604}
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