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Simplifying x(x + 28) = 196 Reorder the terms: x(28 + x) = 196 (28 * x + x * x) = 196 (28x + x2) = 196 Solving 28x + x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 28x + x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 28x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 28x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 28x + x2 = 0 + 196 28x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 28x + x2 = 196 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 = 196 + 196 Reorder the terms: 196 + 28x + x2 = 196 + 196 Combine like terms: 196 + 196 = 392 196 + 28x + x2 = 392 Factor a perfect square on the left side: (x + 14)(x + 14) = 392 Calculate the square root of the right side: 19.798989873 Break this problem into two subproblems by setting (x + 14) equal to 19.798989873 and -19.798989873.Subproblem 1
x + 14 = 19.798989873 Simplifying x + 14 = 19.798989873 Reorder the terms: 14 + x = 19.798989873 Solving 14 + x = 19.798989873 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 = 19.798989873 + -14 Combine like terms: 14 + -14 = 0 0 + x = 19.798989873 + -14 x = 19.798989873 + -14 Combine like terms: 19.798989873 + -14 = 5.798989873 x = 5.798989873 Simplifying x = 5.798989873Subproblem 2
x + 14 = -19.798989873 Simplifying x + 14 = -19.798989873 Reorder the terms: 14 + x = -19.798989873 Solving 14 + x = -19.798989873 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 = -19.798989873 + -14 Combine like terms: 14 + -14 = 0 0 + x = -19.798989873 + -14 x = -19.798989873 + -14 Combine like terms: -19.798989873 + -14 = -33.798989873 x = -33.798989873 Simplifying x = -33.798989873Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.798989873, -33.798989873}
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