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Simplifying (2x2) + 2x + -105 = 0 Reorder the terms: -105 + 2x + (2x2) = 0 Solving -105 + 2x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -52.5 + x + x2 = 0 Move the constant term to the right: Add '52.5' to each side of the equation. -52.5 + x + 52.5 + x2 = 0 + 52.5 Reorder the terms: -52.5 + 52.5 + x + x2 = 0 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x + x2 = 0 + 52.5 x + x2 = 0 + 52.5 Combine like terms: 0 + 52.5 = 52.5 x + x2 = 52.5 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. + 0.25 + x2 = 52.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 52.5 + 0.25 Combine like terms: 52.5 + 0.25 = 52.75 1.25 + x2 = 52.75 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 52.75 Calculate the square root of the right side: 7.262919523 Break this problem into two subproblems by setting ((x) + 0.5) equal to 7.262919523 and -7.262919523.Subproblem 1
(x) + 0.5 = 7.262919523 Simplifying (x) + 0.5 = 7.262919523 x + 0.5 = 7.262919523 Reorder the terms: 0.5 + x = 7.262919523 Solving 0.5 + x = 7.262919523 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 = 7.262919523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.262919523 + -0.5 x = 7.262919523 + -0.5 Combine like terms: 7.262919523 + -0.5 = 6.762919523 x = 6.762919523 Simplifying x = 6.762919523Subproblem 2
(x) + 0.5 = -7.262919523 Simplifying (x) + 0.5 = -7.262919523 x + 0.5 = -7.262919523 Reorder the terms: 0.5 + x = -7.262919523 Solving 0.5 + x = -7.262919523 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 = -7.262919523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.262919523 + -0.5 x = -7.262919523 + -0.5 Combine like terms: -7.262919523 + -0.5 = -7.762919523 x = -7.762919523 Simplifying x = -7.762919523Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.762919523, -7.762919523}
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