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Simplifying 40x2 + -1x + -24 = 0 Reorder the terms: -24 + -1x + 40x2 = 0 Solving -24 + -1x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.6 + -0.025x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.025x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.025x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.025x + x2 = 0 + 0.6 -0.025x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.025x + x2 = 0.6 The x term is -0.025x. Take half its coefficient (-0.0125). Square it (0.00015625) and add it to both sides. Add '0.00015625' to each side of the equation. -0.025x + 0.00015625 + x2 = 0.6 + 0.00015625 Reorder the terms: 0.00015625 + -0.025x + x2 = 0.6 + 0.00015625 Combine like terms: 0.6 + 0.00015625 = 0.60015625 0.00015625 + -0.025x + x2 = 0.60015625 Factor a perfect square on the left side: (x + -0.0125)(x + -0.0125) = 0.60015625 Calculate the square root of the right side: 0.774697522 Break this problem into two subproblems by setting (x + -0.0125) equal to 0.774697522 and -0.774697522.Subproblem 1
x + -0.0125 = 0.774697522 Simplifying x + -0.0125 = 0.774697522 Reorder the terms: -0.0125 + x = 0.774697522 Solving -0.0125 + x = 0.774697522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0125' to each side of the equation. -0.0125 + 0.0125 + x = 0.774697522 + 0.0125 Combine like terms: -0.0125 + 0.0125 = 0.0000 0.0000 + x = 0.774697522 + 0.0125 x = 0.774697522 + 0.0125 Combine like terms: 0.774697522 + 0.0125 = 0.787197522 x = 0.787197522 Simplifying x = 0.787197522Subproblem 2
x + -0.0125 = -0.774697522 Simplifying x + -0.0125 = -0.774697522 Reorder the terms: -0.0125 + x = -0.774697522 Solving -0.0125 + x = -0.774697522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0125' to each side of the equation. -0.0125 + 0.0125 + x = -0.774697522 + 0.0125 Combine like terms: -0.0125 + 0.0125 = 0.0000 0.0000 + x = -0.774697522 + 0.0125 x = -0.774697522 + 0.0125 Combine like terms: -0.774697522 + 0.0125 = -0.762197522 x = -0.762197522 Simplifying x = -0.762197522Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.787197522, -0.762197522}
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