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Simplifying 2x2 + 9x + -28 = 184 Reorder the terms: -28 + 9x + 2x2 = 184 Solving -28 + 9x + 2x2 = 184 Solving for variable 'x'. Reorder the terms: -28 + -184 + 9x + 2x2 = 184 + -184 Combine like terms: -28 + -184 = -212 -212 + 9x + 2x2 = 184 + -184 Combine like terms: 184 + -184 = 0 -212 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -106 + 4.5x + x2 = 0 Move the constant term to the right: Add '106' to each side of the equation. -106 + 4.5x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 4.5x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 4.5x + x2 = 0 + 106 4.5x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 4.5x + x2 = 106 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 106 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 106 + 5.0625 Combine like terms: 106 + 5.0625 = 111.0625 5.0625 + 4.5x + x2 = 111.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 111.0625 Calculate the square root of the right side: 10.538619454 Break this problem into two subproblems by setting (x + 2.25) equal to 10.538619454 and -10.538619454.Subproblem 1
x + 2.25 = 10.538619454 Simplifying x + 2.25 = 10.538619454 Reorder the terms: 2.25 + x = 10.538619454 Solving 2.25 + x = 10.538619454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 10.538619454 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 10.538619454 + -2.25 x = 10.538619454 + -2.25 Combine like terms: 10.538619454 + -2.25 = 8.288619454 x = 8.288619454 Simplifying x = 8.288619454Subproblem 2
x + 2.25 = -10.538619454 Simplifying x + 2.25 = -10.538619454 Reorder the terms: 2.25 + x = -10.538619454 Solving 2.25 + x = -10.538619454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -10.538619454 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -10.538619454 + -2.25 x = -10.538619454 + -2.25 Combine like terms: -10.538619454 + -2.25 = -12.788619454 x = -12.788619454 Simplifying x = -12.788619454Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.288619454, -12.788619454}
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