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Simplifying x2 + -4 = 52 + 3x Reorder the terms: -4 + x2 = 52 + 3x Solving -4 + x2 = 52 + 3x Solving for variable 'x'. Reorder the terms: -4 + -52 + -3x + x2 = 52 + 3x + -52 + -3x Combine like terms: -4 + -52 = -56 -56 + -3x + x2 = 52 + 3x + -52 + -3x Reorder the terms: -56 + -3x + x2 = 52 + -52 + 3x + -3x Combine like terms: 52 + -52 = 0 -56 + -3x + x2 = 0 + 3x + -3x -56 + -3x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -56 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -3x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -3x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -3x + x2 = 0 + 56 -3x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -3x + x2 = 56 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 56 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 56 + 2.25 Combine like terms: 56 + 2.25 = 58.25 2.25 + -3x + x2 = 58.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -1.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + -1.5 = 7.632168761 Simplifying x + -1.5 = 7.632168761 Reorder the terms: -1.5 + x = 7.632168761 Solving -1.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.632168761 + 1.5 x = 7.632168761 + 1.5 Combine like terms: 7.632168761 + 1.5 = 9.132168761 x = 9.132168761 Simplifying x = 9.132168761Subproblem 2
x + -1.5 = -7.632168761 Simplifying x + -1.5 = -7.632168761 Reorder the terms: -1.5 + x = -7.632168761 Solving -1.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.632168761 + 1.5 x = -7.632168761 + 1.5 Combine like terms: -7.632168761 + 1.5 = -6.132168761 x = -6.132168761 Simplifying x = -6.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.132168761, -6.132168761}
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