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Simplifying 0 = 1.5x2 + -4x + -243 Reorder the terms: 0 = -243 + -4x + 1.5x2 Solving 0 = -243 + -4x + 1.5x2 Solving for variable 'x'. Combine like terms: 0 + 243 = 243 243 + 4x + -1.5x2 = -243 + -4x + 1.5x2 + 243 + 4x + -1.5x2 Reorder the terms: 243 + 4x + -1.5x2 = -243 + 243 + -4x + 4x + 1.5x2 + -1.5x2 Combine like terms: -243 + 243 = 0 243 + 4x + -1.5x2 = 0 + -4x + 4x + 1.5x2 + -1.5x2 243 + 4x + -1.5x2 = -4x + 4x + 1.5x2 + -1.5x2 Combine like terms: -4x + 4x = 0 243 + 4x + -1.5x2 = 0 + 1.5x2 + -1.5x2 243 + 4x + -1.5x2 = 1.5x2 + -1.5x2 Combine like terms: 1.5x2 + -1.5x2 = 0.0 243 + 4x + -1.5x2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -162 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '162' to each side of the equation. -162 + -2.666666667x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + -2.666666667x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + -2.666666667x + x2 = 0 + 162 -2.666666667x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 -2.666666667x + x2 = 162 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 = 162 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 162 + 1.777777780 Combine like terms: 162 + 1.777777780 = 163.77777778 1.777777780 + -2.666666667x + x2 = 163.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 163.77777778 Calculate the square root of the right side: 12.797569214 Break this problem into two subproblems by setting (x + -1.333333334) equal to 12.797569214 and -12.797569214.Subproblem 1
x + -1.333333334 = 12.797569214 Simplifying x + -1.333333334 = 12.797569214 Reorder the terms: -1.333333334 + x = 12.797569214 Solving -1.333333334 + x = 12.797569214 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 = 12.797569214 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 12.797569214 + 1.333333334 x = 12.797569214 + 1.333333334 Combine like terms: 12.797569214 + 1.333333334 = 14.130902548 x = 14.130902548 Simplifying x = 14.130902548Subproblem 2
x + -1.333333334 = -12.797569214 Simplifying x + -1.333333334 = -12.797569214 Reorder the terms: -1.333333334 + x = -12.797569214 Solving -1.333333334 + x = -12.797569214 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 = -12.797569214 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -12.797569214 + 1.333333334 x = -12.797569214 + 1.333333334 Combine like terms: -12.797569214 + 1.333333334 = -11.46423588 x = -11.46423588 Simplifying x = -11.46423588Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.130902548, -11.46423588}
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