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Simplifying 10x + 5x2 + -1 = 1 Reorder the terms: -1 + 10x + 5x2 = 1 Solving -1 + 10x + 5x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -1 + 10x + 5x2 = 1 + -1 Combine like terms: -1 + -1 = -2 -2 + 10x + 5x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -2 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2x + x2 = 0 + 0.4 2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2x + x2 = 0.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.4 + 1 Reorder the terms: 1 + 2x + x2 = 0.4 + 1 Combine like terms: 0.4 + 1 = 1.4 1 + 2x + x2 = 1.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (x + 1) equal to 1.183215957 and -1.183215957.Subproblem 1
x + 1 = 1.183215957 Simplifying x + 1 = 1.183215957 Reorder the terms: 1 + x = 1.183215957 Solving 1 + x = 1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.183215957 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.183215957 + -1 x = 1.183215957 + -1 Combine like terms: 1.183215957 + -1 = 0.183215957 x = 0.183215957 Simplifying x = 0.183215957Subproblem 2
x + 1 = -1.183215957 Simplifying x + 1 = -1.183215957 Reorder the terms: 1 + x = -1.183215957 Solving 1 + x = -1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.183215957 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.183215957 + -1 x = -1.183215957 + -1 Combine like terms: -1.183215957 + -1 = -2.183215957 x = -2.183215957 Simplifying x = -2.183215957Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183215957, -2.183215957}
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