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Simplifying 5x * 5x + 2x + -1 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + 2x + -1 = 0 Multiply 5 * 5 25x * x + 2x + -1 = 0 Multiply x * x 25x2 + 2x + -1 = 0 Reorder the terms: -1 + 2x + 25x2 = 0 Solving -1 + 2x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + 0.08x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 0.08x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 0.08x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 0.08x + x2 = 0 + 0.04 0.08x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 0.08x + x2 = 0.04 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = 0.04 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = 0.04 + 0.0016 Combine like terms: 0.04 + 0.0016 = 0.0416 0.0016 + 0.08x + x2 = 0.0416 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = 0.0416 Calculate the square root of the right side: 0.203960781 Break this problem into two subproblems by setting (x + 0.04) equal to 0.203960781 and -0.203960781.Subproblem 1
x + 0.04 = 0.203960781 Simplifying x + 0.04 = 0.203960781 Reorder the terms: 0.04 + x = 0.203960781 Solving 0.04 + x = 0.203960781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 0.203960781 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 0.203960781 + -0.04 x = 0.203960781 + -0.04 Combine like terms: 0.203960781 + -0.04 = 0.163960781 x = 0.163960781 Simplifying x = 0.163960781Subproblem 2
x + 0.04 = -0.203960781 Simplifying x + 0.04 = -0.203960781 Reorder the terms: 0.04 + x = -0.203960781 Solving 0.04 + x = -0.203960781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = -0.203960781 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = -0.203960781 + -0.04 x = -0.203960781 + -0.04 Combine like terms: -0.203960781 + -0.04 = -0.243960781 x = -0.243960781 Simplifying x = -0.243960781Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.163960781, -0.243960781}
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