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Simplifying x2 + 14x = 256 Reorder the terms: 14x + x2 = 256 Solving 14x + x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 14x + x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 14x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 14x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 14x + x2 = 0 + 256 14x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 14x + x2 = 256 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 = 256 + 49 Reorder the terms: 49 + 14x + x2 = 256 + 49 Combine like terms: 256 + 49 = 305 49 + 14x + x2 = 305 Factor a perfect square on the left side: (x + 7)(x + 7) = 305 Calculate the square root of the right side: 17.464249197 Break this problem into two subproblems by setting (x + 7) equal to 17.464249197 and -17.464249197.Subproblem 1
x + 7 = 17.464249197 Simplifying x + 7 = 17.464249197 Reorder the terms: 7 + x = 17.464249197 Solving 7 + x = 17.464249197 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 = 17.464249197 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.464249197 + -7 x = 17.464249197 + -7 Combine like terms: 17.464249197 + -7 = 10.464249197 x = 10.464249197 Simplifying x = 10.464249197Subproblem 2
x + 7 = -17.464249197 Simplifying x + 7 = -17.464249197 Reorder the terms: 7 + x = -17.464249197 Solving 7 + x = -17.464249197 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 = -17.464249197 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.464249197 + -7 x = -17.464249197 + -7 Combine like terms: -17.464249197 + -7 = -24.464249197 x = -24.464249197 Simplifying x = -24.464249197Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.464249197, -24.464249197}
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