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Simplifying 3x2 + -8x + 1.2 = 0 Reorder the terms: 1.2 + -8x + 3x2 = 0 Solving 1.2 + -8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.4 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.666666667x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.666666667x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.666666667x + x2 = 0 + -0.4 -2.666666667x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.666666667x + x2 = -0.4 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -0.4 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -0.4 + 1.777777780 Combine like terms: -0.4 + 1.777777780 = 1.37777778 1.777777780 + -2.666666667x + x2 = 1.37777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.37777778 Calculate the square root of the right side: 1.173787792 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.173787792 and -1.173787792.Subproblem 1
x + -1.333333334 = 1.173787792 Simplifying x + -1.333333334 = 1.173787792 Reorder the terms: -1.333333334 + x = 1.173787792 Solving -1.333333334 + x = 1.173787792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.173787792 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.173787792 + 1.333333334 x = 1.173787792 + 1.333333334 Combine like terms: 1.173787792 + 1.333333334 = 2.507121126 x = 2.507121126 Simplifying x = 2.507121126Subproblem 2
x + -1.333333334 = -1.173787792 Simplifying x + -1.333333334 = -1.173787792 Reorder the terms: -1.333333334 + x = -1.173787792 Solving -1.333333334 + x = -1.173787792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.173787792 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.173787792 + 1.333333334 x = -1.173787792 + 1.333333334 Combine like terms: -1.173787792 + 1.333333334 = 0.159545542 x = 0.159545542 Simplifying x = 0.159545542Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.507121126, 0.159545542}
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