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Simplifying 5x2 + 100x + 3 = 0 Reorder the terms: 3 + 100x + 5x2 = 0 Solving 3 + 100x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 20x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 20x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 20x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 20x + x2 = 0 + -0.6 20x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 20x + x2 = -0.6 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -0.6 + 100 Reorder the terms: 100 + 20x + x2 = -0.6 + 100 Combine like terms: -0.6 + 100 = 99.4 100 + 20x + x2 = 99.4 Factor a perfect square on the left side: (x + 10)(x + 10) = 99.4 Calculate the square root of the right side: 9.969954864 Break this problem into two subproblems by setting (x + 10) equal to 9.969954864 and -9.969954864.Subproblem 1
x + 10 = 9.969954864 Simplifying x + 10 = 9.969954864 Reorder the terms: 10 + x = 9.969954864 Solving 10 + x = 9.969954864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.969954864 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.969954864 + -10 x = 9.969954864 + -10 Combine like terms: 9.969954864 + -10 = -0.030045136 x = -0.030045136 Simplifying x = -0.030045136Subproblem 2
x + 10 = -9.969954864 Simplifying x + 10 = -9.969954864 Reorder the terms: 10 + x = -9.969954864 Solving 10 + x = -9.969954864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.969954864 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.969954864 + -10 x = -9.969954864 + -10 Combine like terms: -9.969954864 + -10 = -19.969954864 x = -19.969954864 Simplifying x = -19.969954864Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.030045136, -19.969954864}
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