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Simplifying 3x2 + 60 = 2x2 + -25x Reorder the terms: 60 + 3x2 = 2x2 + -25x Reorder the terms: 60 + 3x2 = -25x + 2x2 Solving 60 + 3x2 = -25x + 2x2 Solving for variable 'x'. Reorder the terms: 60 + 25x + 3x2 + -2x2 = -25x + 2x2 + 25x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 60 + 25x + 1x2 = -25x + 2x2 + 25x + -2x2 Reorder the terms: 60 + 25x + 1x2 = -25x + 25x + 2x2 + -2x2 Combine like terms: -25x + 25x = 0 60 + 25x + 1x2 = 0 + 2x2 + -2x2 60 + 25x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 60 + 25x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 25x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 25x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 25x + x2 = 0 + -60 25x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 25x + x2 = -60 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -60 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -60 + 156.25 Combine like terms: -60 + 156.25 = 96.25 156.25 + 25x + x2 = 96.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 12.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 12.5 = 9.810708435 Simplifying x + 12.5 = 9.810708435 Reorder the terms: 12.5 + x = 9.810708435 Solving 12.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 9.810708435 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 9.810708435 + -12.5 x = 9.810708435 + -12.5 Combine like terms: 9.810708435 + -12.5 = -2.689291565 x = -2.689291565 Simplifying x = -2.689291565Subproblem 2
x + 12.5 = -9.810708435 Simplifying x + 12.5 = -9.810708435 Reorder the terms: 12.5 + x = -9.810708435 Solving 12.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -9.810708435 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -9.810708435 + -12.5 x = -9.810708435 + -12.5 Combine like terms: -9.810708435 + -12.5 = -22.310708435 x = -22.310708435 Simplifying x = -22.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.689291565, -22.310708435}
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