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Simplifying 0.3x2 + -30x = 0.3 Reorder the terms: -30x + 0.3x2 = 0.3 Solving -30x + 0.3x2 = 0.3 Solving for variable 'x'. Reorder the terms: -0.3 + -30x + 0.3x2 = 0.3 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + -30x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -1 + -100x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -100x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -100x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -100x + x2 = 0 + 1 -100x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -100x + x2 = 1 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 1 + 2500 Reorder the terms: 2500 + -100x + x2 = 1 + 2500 Combine like terms: 1 + 2500 = 2501 2500 + -100x + x2 = 2501 Factor a perfect square on the left side: (x + -50)(x + -50) = 2501 Calculate the square root of the right side: 50.009999 Break this problem into two subproblems by setting (x + -50) equal to 50.009999 and -50.009999.Subproblem 1
x + -50 = 50.009999 Simplifying x + -50 = 50.009999 Reorder the terms: -50 + x = 50.009999 Solving -50 + x = 50.009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 50.009999 + 50 Combine like terms: -50 + 50 = 0 0 + x = 50.009999 + 50 x = 50.009999 + 50 Combine like terms: 50.009999 + 50 = 100.009999 x = 100.009999 Simplifying x = 100.009999Subproblem 2
x + -50 = -50.009999 Simplifying x + -50 = -50.009999 Reorder the terms: -50 + x = -50.009999 Solving -50 + x = -50.009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -50.009999 + 50 Combine like terms: -50 + 50 = 0 0 + x = -50.009999 + 50 x = -50.009999 + 50 Combine like terms: -50.009999 + 50 = -0.009999 x = -0.009999 Simplifying x = -0.009999Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.009999, -0.009999}
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