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Simplifying 2x2 + x = 179 Reorder the terms: x + 2x2 = 179 Solving x + 2x2 = 179 Solving for variable 'x'. Reorder the terms: -179 + x + 2x2 = 179 + -179 Combine like terms: 179 + -179 = 0 -179 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -89.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '89.5' to each side of the equation. -89.5 + 0.5x + 89.5 + x2 = 0 + 89.5 Reorder the terms: -89.5 + 89.5 + 0.5x + x2 = 0 + 89.5 Combine like terms: -89.5 + 89.5 = 0.0 0.0 + 0.5x + x2 = 0 + 89.5 0.5x + x2 = 0 + 89.5 Combine like terms: 0 + 89.5 = 89.5 0.5x + x2 = 89.5 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 = 89.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 89.5 + 0.25 Combine like terms: 89.5 + 0.25 = 89.75 0.25 + 0.5x + x2 = 89.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 89.75 Calculate the square root of the right side: 9.473647661 Break this problem into two subproblems by setting (x + 0.5) equal to 9.473647661 and -9.473647661.Subproblem 1
x + 0.5 = 9.473647661 Simplifying x + 0.5 = 9.473647661 Reorder the terms: 0.5 + x = 9.473647661 Solving 0.5 + x = 9.473647661 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 = 9.473647661 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.473647661 + -0.5 x = 9.473647661 + -0.5 Combine like terms: 9.473647661 + -0.5 = 8.973647661 x = 8.973647661 Simplifying x = 8.973647661Subproblem 2
x + 0.5 = -9.473647661 Simplifying x + 0.5 = -9.473647661 Reorder the terms: 0.5 + x = -9.473647661 Solving 0.5 + x = -9.473647661 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 = -9.473647661 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.473647661 + -0.5 x = -9.473647661 + -0.5 Combine like terms: -9.473647661 + -0.5 = -9.973647661 x = -9.973647661 Simplifying x = -9.973647661Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.973647661, -9.973647661}
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