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Simplifying 3x2 + -300x2 + -20x + 100 = 0 Reorder the terms: 100 + -20x + 3x2 + -300x2 = 0 Combine like terms: 3x2 + -300x2 = -297x2 100 + -20x + -297x2 = 0 Solving 100 + -20x + -297x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -297 the coefficient of the squared term: Divide each side by '-297'. -0.3367003367 + 0.06734006734x + x2 = 0 Move the constant term to the right: Add '0.3367003367' to each side of the equation. -0.3367003367 + 0.06734006734x + 0.3367003367 + x2 = 0 + 0.3367003367 Reorder the terms: -0.3367003367 + 0.3367003367 + 0.06734006734x + x2 = 0 + 0.3367003367 Combine like terms: -0.3367003367 + 0.3367003367 = 0.0000000000 0.0000000000 + 0.06734006734x + x2 = 0 + 0.3367003367 0.06734006734x + x2 = 0 + 0.3367003367 Combine like terms: 0 + 0.3367003367 = 0.3367003367 0.06734006734x + x2 = 0.3367003367 The x term is 0.06734006734x. Take half its coefficient (0.03367003367). Square it (0.001133671167) and add it to both sides. Add '0.001133671167' to each side of the equation. 0.06734006734x + 0.001133671167 + x2 = 0.3367003367 + 0.001133671167 Reorder the terms: 0.001133671167 + 0.06734006734x + x2 = 0.3367003367 + 0.001133671167 Combine like terms: 0.3367003367 + 0.001133671167 = 0.337834007867 0.001133671167 + 0.06734006734x + x2 = 0.337834007867 Factor a perfect square on the left side: (x + 0.03367003367)(x + 0.03367003367) = 0.337834007867 Calculate the square root of the right side: 0.581234899 Break this problem into two subproblems by setting (x + 0.03367003367) equal to 0.581234899 and -0.581234899.Subproblem 1
x + 0.03367003367 = 0.581234899 Simplifying x + 0.03367003367 = 0.581234899 Reorder the terms: 0.03367003367 + x = 0.581234899 Solving 0.03367003367 + x = 0.581234899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03367003367' to each side of the equation. 0.03367003367 + -0.03367003367 + x = 0.581234899 + -0.03367003367 Combine like terms: 0.03367003367 + -0.03367003367 = 0.00000000000 0.00000000000 + x = 0.581234899 + -0.03367003367 x = 0.581234899 + -0.03367003367 Combine like terms: 0.581234899 + -0.03367003367 = 0.54756486533 x = 0.54756486533 Simplifying x = 0.54756486533Subproblem 2
x + 0.03367003367 = -0.581234899 Simplifying x + 0.03367003367 = -0.581234899 Reorder the terms: 0.03367003367 + x = -0.581234899 Solving 0.03367003367 + x = -0.581234899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03367003367' to each side of the equation. 0.03367003367 + -0.03367003367 + x = -0.581234899 + -0.03367003367 Combine like terms: 0.03367003367 + -0.03367003367 = 0.00000000000 0.00000000000 + x = -0.581234899 + -0.03367003367 x = -0.581234899 + -0.03367003367 Combine like terms: -0.581234899 + -0.03367003367 = -0.61490493267 x = -0.61490493267 Simplifying x = -0.61490493267Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.54756486533, -0.61490493267}
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