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Simplifying 1000x2 + 45x + -3.5 = 0 Reorder the terms: -3.5 + 45x + 1000x2 = 0 Solving -3.5 + 45x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.0035 + 0.045x + x2 = 0 Move the constant term to the right: Add '0.0035' to each side of the equation. -0.0035 + 0.045x + 0.0035 + x2 = 0 + 0.0035 Reorder the terms: -0.0035 + 0.0035 + 0.045x + x2 = 0 + 0.0035 Combine like terms: -0.0035 + 0.0035 = 0.0000 0.0000 + 0.045x + x2 = 0 + 0.0035 0.045x + x2 = 0 + 0.0035 Combine like terms: 0 + 0.0035 = 0.0035 0.045x + x2 = 0.0035 The x term is 0.045x. Take half its coefficient (0.0225). Square it (0.00050625) and add it to both sides. Add '0.00050625' to each side of the equation. 0.045x + 0.00050625 + x2 = 0.0035 + 0.00050625 Reorder the terms: 0.00050625 + 0.045x + x2 = 0.0035 + 0.00050625 Combine like terms: 0.0035 + 0.00050625 = 0.00400625 0.00050625 + 0.045x + x2 = 0.00400625 Factor a perfect square on the left side: (x + 0.0225)(x + 0.0225) = 0.00400625 Calculate the square root of the right side: 0.063294945 Break this problem into two subproblems by setting (x + 0.0225) equal to 0.063294945 and -0.063294945.Subproblem 1
x + 0.0225 = 0.063294945 Simplifying x + 0.0225 = 0.063294945 Reorder the terms: 0.0225 + x = 0.063294945 Solving 0.0225 + x = 0.063294945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0225' to each side of the equation. 0.0225 + -0.0225 + x = 0.063294945 + -0.0225 Combine like terms: 0.0225 + -0.0225 = 0.0000 0.0000 + x = 0.063294945 + -0.0225 x = 0.063294945 + -0.0225 Combine like terms: 0.063294945 + -0.0225 = 0.040794945 x = 0.040794945 Simplifying x = 0.040794945Subproblem 2
x + 0.0225 = -0.063294945 Simplifying x + 0.0225 = -0.063294945 Reorder the terms: 0.0225 + x = -0.063294945 Solving 0.0225 + x = -0.063294945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0225' to each side of the equation. 0.0225 + -0.0225 + x = -0.063294945 + -0.0225 Combine like terms: 0.0225 + -0.0225 = 0.0000 0.0000 + x = -0.063294945 + -0.0225 x = -0.063294945 + -0.0225 Combine like terms: -0.063294945 + -0.0225 = -0.085794945 x = -0.085794945 Simplifying x = -0.085794945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.040794945, -0.085794945}
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