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Simplifying x2 + 14x = 400 Reorder the terms: 14x + x2 = 400 Solving 14x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 14x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 14x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 14x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 14x + x2 = 0 + 400 14x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 14x + x2 = 400 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 = 400 + 49 Reorder the terms: 49 + 14x + x2 = 400 + 49 Combine like terms: 400 + 49 = 449 49 + 14x + x2 = 449 Factor a perfect square on the left side: (x + 7)(x + 7) = 449 Calculate the square root of the right side: 21.1896201 Break this problem into two subproblems by setting (x + 7) equal to 21.1896201 and -21.1896201.Subproblem 1
x + 7 = 21.1896201 Simplifying x + 7 = 21.1896201 Reorder the terms: 7 + x = 21.1896201 Solving 7 + x = 21.1896201 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 = 21.1896201 + -7 Combine like terms: 7 + -7 = 0 0 + x = 21.1896201 + -7 x = 21.1896201 + -7 Combine like terms: 21.1896201 + -7 = 14.1896201 x = 14.1896201 Simplifying x = 14.1896201Subproblem 2
x + 7 = -21.1896201 Simplifying x + 7 = -21.1896201 Reorder the terms: 7 + x = -21.1896201 Solving 7 + x = -21.1896201 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 = -21.1896201 + -7 Combine like terms: 7 + -7 = 0 0 + x = -21.1896201 + -7 x = -21.1896201 + -7 Combine like terms: -21.1896201 + -7 = -28.1896201 x = -28.1896201 Simplifying x = -28.1896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.1896201, -28.1896201}
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