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Simplifying 0.3x2 + 20x + -67.5 = 0 Reorder the terms: -67.5 + 20x + 0.3x2 = 0 Solving -67.5 + 20x + 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'. -225 + 66.66666667x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + 66.66666667x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 66.66666667x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 66.66666667x + x2 = 0 + 225 66.66666667x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 66.66666667x + x2 = 225 The x term is 66.66666667x. Take half its coefficient (33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. 66.66666667x + 1111.111112 + x2 = 225 + 1111.111112 Reorder the terms: 1111.111112 + 66.66666667x + x2 = 225 + 1111.111112 Combine like terms: 225 + 1111.111112 = 1336.111112 1111.111112 + 66.66666667x + x2 = 1336.111112 Factor a perfect square on the left side: (x + 33.33333334)(x + 33.33333334) = 1336.111112 Calculate the square root of the right side: 36.552853678 Break this problem into two subproblems by setting (x + 33.33333334) equal to 36.552853678 and -36.552853678.Subproblem 1
x + 33.33333334 = 36.552853678 Simplifying x + 33.33333334 = 36.552853678 Reorder the terms: 33.33333334 + x = 36.552853678 Solving 33.33333334 + x = 36.552853678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = 36.552853678 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = 36.552853678 + -33.33333334 x = 36.552853678 + -33.33333334 Combine like terms: 36.552853678 + -33.33333334 = 3.219520338 x = 3.219520338 Simplifying x = 3.219520338Subproblem 2
x + 33.33333334 = -36.552853678 Simplifying x + 33.33333334 = -36.552853678 Reorder the terms: 33.33333334 + x = -36.552853678 Solving 33.33333334 + x = -36.552853678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = -36.552853678 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = -36.552853678 + -33.33333334 x = -36.552853678 + -33.33333334 Combine like terms: -36.552853678 + -33.33333334 = -69.886187018 x = -69.886187018 Simplifying x = -69.886187018Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.219520338, -69.886187018}
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