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Simplifying 5x2 = x + 132 Reorder the terms: 5x2 = 132 + x Solving 5x2 = 132 + x Solving for variable 'x'. Reorder the terms: -132 + -1x + 5x2 = 132 + x + -132 + -1x Reorder the terms: -132 + -1x + 5x2 = 132 + -132 + x + -1x Combine like terms: 132 + -132 = 0 -132 + -1x + 5x2 = 0 + x + -1x -132 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -132 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -26.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '26.4' to each side of the equation. -26.4 + -0.2x + 26.4 + x2 = 0 + 26.4 Reorder the terms: -26.4 + 26.4 + -0.2x + x2 = 0 + 26.4 Combine like terms: -26.4 + 26.4 = 0.0 0.0 + -0.2x + x2 = 0 + 26.4 -0.2x + x2 = 0 + 26.4 Combine like terms: 0 + 26.4 = 26.4 -0.2x + x2 = 26.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 26.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 26.4 + 0.01 Combine like terms: 26.4 + 0.01 = 26.41 0.01 + -0.2x + x2 = 26.41 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 26.41 Calculate the square root of the right side: 5.139066063 Break this problem into two subproblems by setting (x + -0.1) equal to 5.139066063 and -5.139066063.Subproblem 1
x + -0.1 = 5.139066063 Simplifying x + -0.1 = 5.139066063 Reorder the terms: -0.1 + x = 5.139066063 Solving -0.1 + x = 5.139066063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 5.139066063 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 5.139066063 + 0.1 x = 5.139066063 + 0.1 Combine like terms: 5.139066063 + 0.1 = 5.239066063 x = 5.239066063 Simplifying x = 5.239066063Subproblem 2
x + -0.1 = -5.139066063 Simplifying x + -0.1 = -5.139066063 Reorder the terms: -0.1 + x = -5.139066063 Solving -0.1 + x = -5.139066063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -5.139066063 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -5.139066063 + 0.1 x = -5.139066063 + 0.1 Combine like terms: -5.139066063 + 0.1 = -5.039066063 x = -5.039066063 Simplifying x = -5.039066063Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.239066063, -5.039066063}
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