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Simplifying 2x2 + x = 0.925 Reorder the terms: x + 2x2 = 0.925 Solving x + 2x2 = 0.925 Solving for variable 'x'. Reorder the terms: -0.925 + x + 2x2 = 0.925 + -0.925 Combine like terms: 0.925 + -0.925 = 0.000 -0.925 + x + 2x2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.4625 + 0.5x + x2 = 0.000 Move the constant term to the right: Add '0.4625' to each side of the equation. -0.4625 + 0.5x + 0.4625 + x2 = 0.000 + 0.4625 Reorder the terms: -0.4625 + 0.4625 + 0.5x + x2 = 0.000 + 0.4625 Combine like terms: -0.4625 + 0.4625 = 0.0000 0.0000 + 0.5x + x2 = 0.000 + 0.4625 0.5x + x2 = 0.000 + 0.4625 Combine like terms: 0.000 + 0.4625 = 0.4625 0.5x + x2 = 0.4625 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 = 0.4625 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 0.4625 + 0.25 Combine like terms: 0.4625 + 0.25 = 0.7125 0.25 + 0.5x + x2 = 0.7125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.7125 Calculate the square root of the right side: 0.844097151 Break this problem into two subproblems by setting (x + 0.5) equal to 0.844097151 and -0.844097151.Subproblem 1
x + 0.5 = 0.844097151 Simplifying x + 0.5 = 0.844097151 Reorder the terms: 0.5 + x = 0.844097151 Solving 0.5 + x = 0.844097151 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 = 0.844097151 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.844097151 + -0.5 x = 0.844097151 + -0.5 Combine like terms: 0.844097151 + -0.5 = 0.344097151 x = 0.344097151 Simplifying x = 0.344097151Subproblem 2
x + 0.5 = -0.844097151 Simplifying x + 0.5 = -0.844097151 Reorder the terms: 0.5 + x = -0.844097151 Solving 0.5 + x = -0.844097151 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 = -0.844097151 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.844097151 + -0.5 x = -0.844097151 + -0.5 Combine like terms: -0.844097151 + -0.5 = -1.344097151 x = -1.344097151 Simplifying x = -1.344097151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.344097151, -1.344097151}
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