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Simplifying 5x2 + 3x + 2 = 1240 Reorder the terms: 2 + 3x + 5x2 = 1240 Solving 2 + 3x + 5x2 = 1240 Solving for variable 'x'. Reorder the terms: 2 + -1240 + 3x + 5x2 = 1240 + -1240 Combine like terms: 2 + -1240 = -1238 -1238 + 3x + 5x2 = 1240 + -1240 Combine like terms: 1240 + -1240 = 0 -1238 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -247.6 + 0.6x + x2 = 0 Move the constant term to the right: Add '247.6' to each side of the equation. -247.6 + 0.6x + 247.6 + x2 = 0 + 247.6 Reorder the terms: -247.6 + 247.6 + 0.6x + x2 = 0 + 247.6 Combine like terms: -247.6 + 247.6 = 0.0 0.0 + 0.6x + x2 = 0 + 247.6 0.6x + x2 = 0 + 247.6 Combine like terms: 0 + 247.6 = 247.6 0.6x + x2 = 247.6 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 247.6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 247.6 + 0.09 Combine like terms: 247.6 + 0.09 = 247.69 0.09 + 0.6x + x2 = 247.69 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 247.69 Calculate the square root of the right side: 15.73817016 Break this problem into two subproblems by setting (x + 0.3) equal to 15.73817016 and -15.73817016.Subproblem 1
x + 0.3 = 15.73817016 Simplifying x + 0.3 = 15.73817016 Reorder the terms: 0.3 + x = 15.73817016 Solving 0.3 + x = 15.73817016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 15.73817016 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 15.73817016 + -0.3 x = 15.73817016 + -0.3 Combine like terms: 15.73817016 + -0.3 = 15.43817016 x = 15.43817016 Simplifying x = 15.43817016Subproblem 2
x + 0.3 = -15.73817016 Simplifying x + 0.3 = -15.73817016 Reorder the terms: 0.3 + x = -15.73817016 Solving 0.3 + x = -15.73817016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -15.73817016 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -15.73817016 + -0.3 x = -15.73817016 + -0.3 Combine like terms: -15.73817016 + -0.3 = -16.03817016 x = -16.03817016 Simplifying x = -16.03817016Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.43817016, -16.03817016}
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