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Simplifying 2 = 5x2 + -10x Reorder the terms: 2 = -10x + 5x2 Solving 2 = -10x + 5x2 Solving for variable 'x'. Reorder the terms: 2 + 10x + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 2 + 10x + -5x2 = 0 + 5x2 + -5x2 2 + 10x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 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 = 2.183215957 x = 2.183215957 Simplifying x = 2.183215957Subproblem 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 = -0.183215957 x = -0.183215957 Simplifying x = -0.183215957Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.183215957, -0.183215957}
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