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Simplifying 0 = 100x2 + -30.7x + -184 Reorder the terms: 0 = -184 + -30.7x + 100x2 Solving 0 = -184 + -30.7x + 100x2 Solving for variable 'x'. Combine like terms: 0 + 184 = 184 184 + 30.7x + -100x2 = -184 + -30.7x + 100x2 + 184 + 30.7x + -100x2 Reorder the terms: 184 + 30.7x + -100x2 = -184 + 184 + -30.7x + 30.7x + 100x2 + -100x2 Combine like terms: -184 + 184 = 0 184 + 30.7x + -100x2 = 0 + -30.7x + 30.7x + 100x2 + -100x2 184 + 30.7x + -100x2 = -30.7x + 30.7x + 100x2 + -100x2 Combine like terms: -30.7x + 30.7x = 0.0 184 + 30.7x + -100x2 = 0.0 + 100x2 + -100x2 184 + 30.7x + -100x2 = 100x2 + -100x2 Combine like terms: 100x2 + -100x2 = 0 184 + 30.7x + -100x2 = 0 Begin completing the square. Divide all terms by -100 the coefficient of the squared term: Divide each side by '-100'. -1.84 + -0.307x + x2 = 0 Move the constant term to the right: Add '1.84' to each side of the equation. -1.84 + -0.307x + 1.84 + x2 = 0 + 1.84 Reorder the terms: -1.84 + 1.84 + -0.307x + x2 = 0 + 1.84 Combine like terms: -1.84 + 1.84 = 0.00 0.00 + -0.307x + x2 = 0 + 1.84 -0.307x + x2 = 0 + 1.84 Combine like terms: 0 + 1.84 = 1.84 -0.307x + x2 = 1.84 The x term is -0.307x. Take half its coefficient (-0.1535). Square it (0.02356225) and add it to both sides. Add '0.02356225' to each side of the equation. -0.307x + 0.02356225 + x2 = 1.84 + 0.02356225 Reorder the terms: 0.02356225 + -0.307x + x2 = 1.84 + 0.02356225 Combine like terms: 1.84 + 0.02356225 = 1.86356225 0.02356225 + -0.307x + x2 = 1.86356225 Factor a perfect square on the left side: (x + -0.1535)(x + -0.1535) = 1.86356225 Calculate the square root of the right side: 1.365123529 Break this problem into two subproblems by setting (x + -0.1535) equal to 1.365123529 and -1.365123529.Subproblem 1
x + -0.1535 = 1.365123529 Simplifying x + -0.1535 = 1.365123529 Reorder the terms: -0.1535 + x = 1.365123529 Solving -0.1535 + x = 1.365123529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1535' to each side of the equation. -0.1535 + 0.1535 + x = 1.365123529 + 0.1535 Combine like terms: -0.1535 + 0.1535 = 0.0000 0.0000 + x = 1.365123529 + 0.1535 x = 1.365123529 + 0.1535 Combine like terms: 1.365123529 + 0.1535 = 1.518623529 x = 1.518623529 Simplifying x = 1.518623529Subproblem 2
x + -0.1535 = -1.365123529 Simplifying x + -0.1535 = -1.365123529 Reorder the terms: -0.1535 + x = -1.365123529 Solving -0.1535 + x = -1.365123529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1535' to each side of the equation. -0.1535 + 0.1535 + x = -1.365123529 + 0.1535 Combine like terms: -0.1535 + 0.1535 = 0.0000 0.0000 + x = -1.365123529 + 0.1535 x = -1.365123529 + 0.1535 Combine like terms: -1.365123529 + 0.1535 = -1.211623529 x = -1.211623529 Simplifying x = -1.211623529Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.518623529, -1.211623529}
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