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Simplifying x2 + -4x + -7.5 = 0 Reorder the terms: -7.5 + -4x + x2 = 0 Solving -7.5 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -4x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -4x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -4x + x2 = 0 + 7.5 -4x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -4x + x2 = 7.5 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 = 7.5 + 4 Reorder the terms: 4 + -4x + x2 = 7.5 + 4 Combine like terms: 7.5 + 4 = 11.5 4 + -4x + x2 = 11.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -2) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -2 = 3.391164992 Simplifying x + -2 = 3.391164992 Reorder the terms: -2 + x = 3.391164992 Solving -2 + x = 3.391164992 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 = 3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.391164992 + 2 x = 3.391164992 + 2 Combine like terms: 3.391164992 + 2 = 5.391164992 x = 5.391164992 Simplifying x = 5.391164992Subproblem 2
x + -2 = -3.391164992 Simplifying x + -2 = -3.391164992 Reorder the terms: -2 + x = -3.391164992 Solving -2 + x = -3.391164992 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 = -3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.391164992 + 2 x = -3.391164992 + 2 Combine like terms: -3.391164992 + 2 = -1.391164992 x = -1.391164992 Simplifying x = -1.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.391164992, -1.391164992}
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