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Simplifying 2x2 + x + -3 = 180 Reorder the terms: -3 + x + 2x2 = 180 Solving -3 + x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + x + 2x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -91.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '91.5' to each side of the equation. -91.5 + 0.5x + 91.5 + x2 = 0 + 91.5 Reorder the terms: -91.5 + 91.5 + 0.5x + x2 = 0 + 91.5 Combine like terms: -91.5 + 91.5 = 0.0 0.0 + 0.5x + x2 = 0 + 91.5 0.5x + x2 = 0 + 91.5 Combine like terms: 0 + 91.5 = 91.5 0.5x + x2 = 91.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 91.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 91.5 + 0.25 Combine like terms: 91.5 + 0.25 = 91.75 0.25 + 0.5x + x2 = 91.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 91.75 Calculate the square root of the right side: 9.57862203 Break this problem into two subproblems by setting (x + 0.5) equal to 9.57862203 and -9.57862203.Subproblem 1
x + 0.5 = 9.57862203 Simplifying x + 0.5 = 9.57862203 Reorder the terms: 0.5 + x = 9.57862203 Solving 0.5 + x = 9.57862203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.57862203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.57862203 + -0.5 x = 9.57862203 + -0.5 Combine like terms: 9.57862203 + -0.5 = 9.07862203 x = 9.07862203 Simplifying x = 9.07862203Subproblem 2
x + 0.5 = -9.57862203 Simplifying x + 0.5 = -9.57862203 Reorder the terms: 0.5 + x = -9.57862203 Solving 0.5 + x = -9.57862203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.57862203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.57862203 + -0.5 x = -9.57862203 + -0.5 Combine like terms: -9.57862203 + -0.5 = -10.07862203 x = -10.07862203 Simplifying x = -10.07862203Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.07862203, -10.07862203}
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