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Simplifying x2 + -4x = 28 Reorder the terms: -4x + x2 = 28 Solving -4x + x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -4x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -4x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -4x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -4x + x2 = 0 + 28 -4x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -4x + x2 = 28 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 + 4 Reorder the terms: 4 + -4x + x2 = 28 + 4 Combine like terms: 28 + 4 = 32 4 + -4x + x2 = 32 Factor a perfect square on the left side: (x + -2)(x + -2) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -2) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -2 = 5.656854249 Simplifying x + -2 = 5.656854249 Reorder the terms: -2 + x = 5.656854249 Solving -2 + x = 5.656854249 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 = 5.656854249 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.656854249 + 2 x = 5.656854249 + 2 Combine like terms: 5.656854249 + 2 = 7.656854249 x = 7.656854249 Simplifying x = 7.656854249Subproblem 2
x + -2 = -5.656854249 Simplifying x + -2 = -5.656854249 Reorder the terms: -2 + x = -5.656854249 Solving -2 + x = -5.656854249 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 = -5.656854249 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.656854249 + 2 x = -5.656854249 + 2 Combine like terms: -5.656854249 + 2 = -3.656854249 x = -3.656854249 Simplifying x = -3.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.656854249, -3.656854249}
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