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Simplifying 5x2 + -15x + -216 = 0 Reorder the terms: -216 + -15x + 5x2 = 0 Solving -216 + -15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -43.2 + -3x + x2 = 0 Move the constant term to the right: Add '43.2' to each side of the equation. -43.2 + -3x + 43.2 + x2 = 0 + 43.2 Reorder the terms: -43.2 + 43.2 + -3x + x2 = 0 + 43.2 Combine like terms: -43.2 + 43.2 = 0.0 0.0 + -3x + x2 = 0 + 43.2 -3x + x2 = 0 + 43.2 Combine like terms: 0 + 43.2 = 43.2 -3x + x2 = 43.2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 43.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 43.2 + 2.25 Combine like terms: 43.2 + 2.25 = 45.45 2.25 + -3x + x2 = 45.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 45.45 Calculate the square root of the right side: 6.741661516 Break this problem into two subproblems by setting (x + -1.5) equal to 6.741661516 and -6.741661516.Subproblem 1
x + -1.5 = 6.741661516 Simplifying x + -1.5 = 6.741661516 Reorder the terms: -1.5 + x = 6.741661516 Solving -1.5 + x = 6.741661516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.741661516 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.741661516 + 1.5 x = 6.741661516 + 1.5 Combine like terms: 6.741661516 + 1.5 = 8.241661516 x = 8.241661516 Simplifying x = 8.241661516Subproblem 2
x + -1.5 = -6.741661516 Simplifying x + -1.5 = -6.741661516 Reorder the terms: -1.5 + x = -6.741661516 Solving -1.5 + x = -6.741661516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.741661516 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.741661516 + 1.5 x = -6.741661516 + 1.5 Combine like terms: -6.741661516 + 1.5 = -5.241661516 x = -5.241661516 Simplifying x = -5.241661516Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.241661516, -5.241661516}
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