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Simplifying 5x2 + 10x + -1 = 0 Reorder the terms: -1 + 10x + 5x2 = 0 Solving -1 + 10x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 2x + x2 = 0 + 0.2 2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 2x + x2 = 0.2 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 = 0.2 + 1 Reorder the terms: 1 + 2x + x2 = 0.2 + 1 Combine like terms: 0.2 + 1 = 1.2 1 + 2x + x2 = 1.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + 1) equal to 1.095445115 and -1.095445115.Subproblem 1
x + 1 = 1.095445115 Simplifying x + 1 = 1.095445115 Reorder the terms: 1 + x = 1.095445115 Solving 1 + x = 1.095445115 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 = 1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.095445115 + -1 x = 1.095445115 + -1 Combine like terms: 1.095445115 + -1 = 0.095445115 x = 0.095445115 Simplifying x = 0.095445115Subproblem 2
x + 1 = -1.095445115 Simplifying x + 1 = -1.095445115 Reorder the terms: 1 + x = -1.095445115 Solving 1 + x = -1.095445115 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 = -1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.095445115 + -1 x = -1.095445115 + -1 Combine like terms: -1.095445115 + -1 = -2.095445115 x = -2.095445115 Simplifying x = -2.095445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.095445115, -2.095445115}
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