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Simplifying 5x2 + 2x = 125 Reorder the terms: 2x + 5x2 = 125 Solving 2x + 5x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 2x + 5x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25 + 0.4x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.4x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 0.4x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.4x + x2 = 0 + 25 0.4x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.4x + x2 = 25 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 25 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 25 + 0.04 Combine like terms: 25 + 0.04 = 25.04 0.04 + 0.4x + x2 = 25.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 25.04 Calculate the square root of the right side: 5.003998401 Break this problem into two subproblems by setting (x + 0.2) equal to 5.003998401 and -5.003998401.Subproblem 1
x + 0.2 = 5.003998401 Simplifying x + 0.2 = 5.003998401 Reorder the terms: 0.2 + x = 5.003998401 Solving 0.2 + x = 5.003998401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 5.003998401 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 5.003998401 + -0.2 x = 5.003998401 + -0.2 Combine like terms: 5.003998401 + -0.2 = 4.803998401 x = 4.803998401 Simplifying x = 4.803998401Subproblem 2
x + 0.2 = -5.003998401 Simplifying x + 0.2 = -5.003998401 Reorder the terms: 0.2 + x = -5.003998401 Solving 0.2 + x = -5.003998401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -5.003998401 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -5.003998401 + -0.2 x = -5.003998401 + -0.2 Combine like terms: -5.003998401 + -0.2 = -5.203998401 x = -5.203998401 Simplifying x = -5.203998401Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.803998401, -5.203998401}
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