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Simplifying 1.2x2 + 3.5x + -1.5 = 0 Reorder the terms: -1.5 + 3.5x + 1.2x2 = 0 Solving -1.5 + 3.5x + 1.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. -1.25 + 2.916666667x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.916666667x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.916666667x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.916666667x + x2 = 0 + 1.25 2.916666667x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.916666667x + x2 = 1.25 The x term is 2.916666667x. Take half its coefficient (1.458333334). Square it (2.126736113) and add it to both sides. Add '2.126736113' to each side of the equation. 2.916666667x + 2.126736113 + x2 = 1.25 + 2.126736113 Reorder the terms: 2.126736113 + 2.916666667x + x2 = 1.25 + 2.126736113 Combine like terms: 1.25 + 2.126736113 = 3.376736113 2.126736113 + 2.916666667x + x2 = 3.376736113 Factor a perfect square on the left side: (x + 1.458333334)(x + 1.458333334) = 3.376736113 Calculate the square root of the right side: 1.837589756 Break this problem into two subproblems by setting (x + 1.458333334) equal to 1.837589756 and -1.837589756.Subproblem 1
x + 1.458333334 = 1.837589756 Simplifying x + 1.458333334 = 1.837589756 Reorder the terms: 1.458333334 + x = 1.837589756 Solving 1.458333334 + x = 1.837589756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = 1.837589756 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = 1.837589756 + -1.458333334 x = 1.837589756 + -1.458333334 Combine like terms: 1.837589756 + -1.458333334 = 0.379256422 x = 0.379256422 Simplifying x = 0.379256422Subproblem 2
x + 1.458333334 = -1.837589756 Simplifying x + 1.458333334 = -1.837589756 Reorder the terms: 1.458333334 + x = -1.837589756 Solving 1.458333334 + x = -1.837589756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = -1.837589756 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = -1.837589756 + -1.458333334 x = -1.837589756 + -1.458333334 Combine like terms: -1.837589756 + -1.458333334 = -3.29592309 x = -3.29592309 Simplifying x = -3.29592309Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.379256422, -3.29592309}
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