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Simplifying 22x2 + 3x + -100 = 0 Reorder the terms: -100 + 3x + 22x2 = 0 Solving -100 + 3x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -4.545454545 + 0.1363636364x + x2 = 0 Move the constant term to the right: Add '4.545454545' to each side of the equation. -4.545454545 + 0.1363636364x + 4.545454545 + x2 = 0 + 4.545454545 Reorder the terms: -4.545454545 + 4.545454545 + 0.1363636364x + x2 = 0 + 4.545454545 Combine like terms: -4.545454545 + 4.545454545 = 0.000000000 0.000000000 + 0.1363636364x + x2 = 0 + 4.545454545 0.1363636364x + x2 = 0 + 4.545454545 Combine like terms: 0 + 4.545454545 = 4.545454545 0.1363636364x + x2 = 4.545454545 The x term is 0.1363636364x. Take half its coefficient (0.0681818182). Square it (0.004648760333) and add it to both sides. Add '0.004648760333' to each side of the equation. 0.1363636364x + 0.004648760333 + x2 = 4.545454545 + 0.004648760333 Reorder the terms: 0.004648760333 + 0.1363636364x + x2 = 4.545454545 + 0.004648760333 Combine like terms: 4.545454545 + 0.004648760333 = 4.550103305333 0.004648760333 + 0.1363636364x + x2 = 4.550103305333 Factor a perfect square on the left side: (x + 0.0681818182)(x + 0.0681818182) = 4.550103305333 Calculate the square root of the right side: 2.133097116 Break this problem into two subproblems by setting (x + 0.0681818182) equal to 2.133097116 and -2.133097116.Subproblem 1
x + 0.0681818182 = 2.133097116 Simplifying x + 0.0681818182 = 2.133097116 Reorder the terms: 0.0681818182 + x = 2.133097116 Solving 0.0681818182 + x = 2.133097116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0681818182' to each side of the equation. 0.0681818182 + -0.0681818182 + x = 2.133097116 + -0.0681818182 Combine like terms: 0.0681818182 + -0.0681818182 = 0.0000000000 0.0000000000 + x = 2.133097116 + -0.0681818182 x = 2.133097116 + -0.0681818182 Combine like terms: 2.133097116 + -0.0681818182 = 2.0649152978 x = 2.0649152978 Simplifying x = 2.0649152978Subproblem 2
x + 0.0681818182 = -2.133097116 Simplifying x + 0.0681818182 = -2.133097116 Reorder the terms: 0.0681818182 + x = -2.133097116 Solving 0.0681818182 + x = -2.133097116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0681818182' to each side of the equation. 0.0681818182 + -0.0681818182 + x = -2.133097116 + -0.0681818182 Combine like terms: 0.0681818182 + -0.0681818182 = 0.0000000000 0.0000000000 + x = -2.133097116 + -0.0681818182 x = -2.133097116 + -0.0681818182 Combine like terms: -2.133097116 + -0.0681818182 = -2.2012789342 x = -2.2012789342 Simplifying x = -2.2012789342Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0649152978, -2.2012789342}
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