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Simplifying (2x2) + -3x = (x2) + 72 Reorder the terms: -3x + (2x2) = (x2) + 72 -3x + (2x2) = x2 + 72 Reorder the terms: -3x + (2x2) = 72 + x2 Solving -3x + (2x2) = 72 + x2 Solving for variable 'x'. Reorder the terms: -72 + -3x + (2x2) + -1x2 = 72 + x2 + -72 + -1x2 Combine like terms: (2x2) + -1x2 = 1x2 -72 + -3x + 1x2 = 72 + x2 + -72 + -1x2 Reorder the terms: -72 + -3x + 1x2 = 72 + -72 + x2 + -1x2 Combine like terms: 72 + -72 = 0 -72 + -3x + 1x2 = 0 + x2 + -1x2 -72 + -3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -72 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -3x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -3x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -3x + x2 = 0 + 72 -3x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -3x + x2 = 72 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 = 72 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 72 + 2.25 Combine like terms: 72 + 2.25 = 74.25 2.25 + -3x + x2 = 74.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -1.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -1.5 = 8.61684397 Simplifying x + -1.5 = 8.61684397 Reorder the terms: -1.5 + x = 8.61684397 Solving -1.5 + x = 8.61684397 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 = 8.61684397 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.61684397 + 1.5 x = 8.61684397 + 1.5 Combine like terms: 8.61684397 + 1.5 = 10.11684397 x = 10.11684397 Simplifying x = 10.11684397Subproblem 2
x + -1.5 = -8.61684397 Simplifying x + -1.5 = -8.61684397 Reorder the terms: -1.5 + x = -8.61684397 Solving -1.5 + x = -8.61684397 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 = -8.61684397 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.61684397 + 1.5 x = -8.61684397 + 1.5 Combine like terms: -8.61684397 + 1.5 = -7.11684397 x = -7.11684397 Simplifying x = -7.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.11684397, -7.11684397}
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