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Simplifying x2 + 14x = 900 Reorder the terms: 14x + x2 = 900 Solving 14x + x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 14x + x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 14x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 14x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 14x + x2 = 0 + 900 14x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 14x + x2 = 900 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 = 900 + 49 Reorder the terms: 49 + 14x + x2 = 900 + 49 Combine like terms: 900 + 49 = 949 49 + 14x + x2 = 949 Factor a perfect square on the left side: (x + 7)(x + 7) = 949 Calculate the square root of the right side: 30.805843601 Break this problem into two subproblems by setting (x + 7) equal to 30.805843601 and -30.805843601.Subproblem 1
x + 7 = 30.805843601 Simplifying x + 7 = 30.805843601 Reorder the terms: 7 + x = 30.805843601 Solving 7 + x = 30.805843601 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 = 30.805843601 + -7 Combine like terms: 7 + -7 = 0 0 + x = 30.805843601 + -7 x = 30.805843601 + -7 Combine like terms: 30.805843601 + -7 = 23.805843601 x = 23.805843601 Simplifying x = 23.805843601Subproblem 2
x + 7 = -30.805843601 Simplifying x + 7 = -30.805843601 Reorder the terms: 7 + x = -30.805843601 Solving 7 + x = -30.805843601 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 = -30.805843601 + -7 Combine like terms: 7 + -7 = 0 0 + x = -30.805843601 + -7 x = -30.805843601 + -7 Combine like terms: -30.805843601 + -7 = -37.805843601 x = -37.805843601 Simplifying x = -37.805843601Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.805843601, -37.805843601}
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