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Simplifying x2 + 28x + 144 = 0 Reorder the terms: 144 + 28x + x2 = 0 Solving 144 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + 28x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + 28x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + 28x + x2 = 0 + -144 28x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 28x + x2 = -144 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -144 + 196 Reorder the terms: 196 + 28x + x2 = -144 + 196 Combine like terms: -144 + 196 = 52 196 + 28x + x2 = 52 Factor a perfect square on the left side: (x + 14)(x + 14) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 14) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 14 = 7.211102551 Simplifying x + 14 = 7.211102551 Reorder the terms: 14 + x = 7.211102551 Solving 14 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 7.211102551 + -14 Combine like terms: 14 + -14 = 0 0 + x = 7.211102551 + -14 x = 7.211102551 + -14 Combine like terms: 7.211102551 + -14 = -6.788897449 x = -6.788897449 Simplifying x = -6.788897449Subproblem 2
x + 14 = -7.211102551 Simplifying x + 14 = -7.211102551 Reorder the terms: 14 + x = -7.211102551 Solving 14 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -7.211102551 + -14 Combine like terms: 14 + -14 = 0 0 + x = -7.211102551 + -14 x = -7.211102551 + -14 Combine like terms: -7.211102551 + -14 = -21.211102551 x = -21.211102551 Simplifying x = -21.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.788897449, -21.211102551}
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