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Simplifying (x + 14)(x) = 300 Reorder the terms: (14 + x)(x) = 300 Reorder the terms for easier multiplication: x(14 + x) = 300 (14 * x + x * x) = 300 (14x + x2) = 300 Solving 14x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 14x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 14x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 14x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 14x + x2 = 0 + 300 14x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 14x + x2 = 300 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 = 300 + 49 Reorder the terms: 49 + 14x + x2 = 300 + 49 Combine like terms: 300 + 49 = 349 49 + 14x + x2 = 349 Factor a perfect square on the left side: (x + 7)(x + 7) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + 7) equal to 18.681541692 and -18.681541692.Subproblem 1
x + 7 = 18.681541692 Simplifying x + 7 = 18.681541692 Reorder the terms: 7 + x = 18.681541692 Solving 7 + x = 18.681541692 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 = 18.681541692 + -7 Combine like terms: 7 + -7 = 0 0 + x = 18.681541692 + -7 x = 18.681541692 + -7 Combine like terms: 18.681541692 + -7 = 11.681541692 x = 11.681541692 Simplifying x = 11.681541692Subproblem 2
x + 7 = -18.681541692 Simplifying x + 7 = -18.681541692 Reorder the terms: 7 + x = -18.681541692 Solving 7 + x = -18.681541692 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 = -18.681541692 + -7 Combine like terms: 7 + -7 = 0 0 + x = -18.681541692 + -7 x = -18.681541692 + -7 Combine like terms: -18.681541692 + -7 = -25.681541692 x = -25.681541692 Simplifying x = -25.681541692Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.681541692, -25.681541692}
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