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Simplifying x2 + 28x + -84 = 0 Reorder the terms: -84 + 28x + x2 = 0 Solving -84 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 28x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 28x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 28x + x2 = 0 + 84 28x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 28x + x2 = 84 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 = 84 + 196 Reorder the terms: 196 + 28x + x2 = 84 + 196 Combine like terms: 84 + 196 = 280 196 + 28x + x2 = 280 Factor a perfect square on the left side: (x + 14)(x + 14) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 14) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 14 = 16.733200531 Simplifying x + 14 = 16.733200531 Reorder the terms: 14 + x = 16.733200531 Solving 14 + x = 16.733200531 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 = 16.733200531 + -14 Combine like terms: 14 + -14 = 0 0 + x = 16.733200531 + -14 x = 16.733200531 + -14 Combine like terms: 16.733200531 + -14 = 2.733200531 x = 2.733200531 Simplifying x = 2.733200531Subproblem 2
x + 14 = -16.733200531 Simplifying x + 14 = -16.733200531 Reorder the terms: 14 + x = -16.733200531 Solving 14 + x = -16.733200531 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 = -16.733200531 + -14 Combine like terms: 14 + -14 = 0 0 + x = -16.733200531 + -14 x = -16.733200531 + -14 Combine like terms: -16.733200531 + -14 = -30.733200531 x = -30.733200531 Simplifying x = -30.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.733200531, -30.733200531}
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