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Simplifying x2 + 4x = 28.8 Reorder the terms: 4x + x2 = 28.8 Solving 4x + x2 = 28.8 Solving for variable 'x'. Reorder the terms: -28.8 + 4x + x2 = 28.8 + -28.8 Combine like terms: 28.8 + -28.8 = 0.0 -28.8 + 4x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + 4x + 28.8 + x2 = 0.0 + 28.8 Reorder the terms: -28.8 + 28.8 + 4x + x2 = 0.0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + 4x + x2 = 0.0 + 28.8 4x + x2 = 0.0 + 28.8 Combine like terms: 0.0 + 28.8 = 28.8 4x + x2 = 28.8 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 28.8 + 4 Reorder the terms: 4 + 4x + x2 = 28.8 + 4 Combine like terms: 28.8 + 4 = 32.8 4 + 4x + x2 = 32.8 Factor a perfect square on the left side: (x + 2)(x + 2) = 32.8 Calculate the square root of the right side: 5.727128425 Break this problem into two subproblems by setting (x + 2) equal to 5.727128425 and -5.727128425.Subproblem 1
x + 2 = 5.727128425 Simplifying x + 2 = 5.727128425 Reorder the terms: 2 + x = 5.727128425 Solving 2 + x = 5.727128425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.727128425 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.727128425 + -2 x = 5.727128425 + -2 Combine like terms: 5.727128425 + -2 = 3.727128425 x = 3.727128425 Simplifying x = 3.727128425Subproblem 2
x + 2 = -5.727128425 Simplifying x + 2 = -5.727128425 Reorder the terms: 2 + x = -5.727128425 Solving 2 + x = -5.727128425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.727128425 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.727128425 + -2 x = -5.727128425 + -2 Combine like terms: -5.727128425 + -2 = -7.727128425 x = -7.727128425 Simplifying x = -7.727128425Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.727128425, -7.727128425}
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