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Simplifying 0.3x2 + 45x + 2 = 0 Reorder the terms: 2 + 45x + 0.3x2 = 0 Solving 2 + 45x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 6.666666667 + 150x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 150x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 150x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 150x + x2 = 0 + -6.666666667 150x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 150x + x2 = -6.666666667 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = -6.666666667 + 5625 Reorder the terms: 5625 + 150x + x2 = -6.666666667 + 5625 Combine like terms: -6.666666667 + 5625 = 5618.333333333 5625 + 150x + x2 = 5618.333333333 Factor a perfect square on the left side: (x + 75)(x + 75) = 5618.333333333 Calculate the square root of the right side: 74.955542379 Break this problem into two subproblems by setting (x + 75) equal to 74.955542379 and -74.955542379.Subproblem 1
x + 75 = 74.955542379 Simplifying x + 75 = 74.955542379 Reorder the terms: 75 + x = 74.955542379 Solving 75 + x = 74.955542379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 74.955542379 + -75 Combine like terms: 75 + -75 = 0 0 + x = 74.955542379 + -75 x = 74.955542379 + -75 Combine like terms: 74.955542379 + -75 = -0.044457621 x = -0.044457621 Simplifying x = -0.044457621Subproblem 2
x + 75 = -74.955542379 Simplifying x + 75 = -74.955542379 Reorder the terms: 75 + x = -74.955542379 Solving 75 + x = -74.955542379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -74.955542379 + -75 Combine like terms: 75 + -75 = 0 0 + x = -74.955542379 + -75 x = -74.955542379 + -75 Combine like terms: -74.955542379 + -75 = -149.955542379 x = -149.955542379 Simplifying x = -149.955542379Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.044457621, -149.955542379}
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