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Simplifying 5x2 + -15x + -81 = 0 Reorder the terms: -81 + -15x + 5x2 = 0 Solving -81 + -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'. -16.2 + -3x + x2 = 0 Move the constant term to the right: Add '16.2' to each side of the equation. -16.2 + -3x + 16.2 + x2 = 0 + 16.2 Reorder the terms: -16.2 + 16.2 + -3x + x2 = 0 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + -3x + x2 = 0 + 16.2 -3x + x2 = 0 + 16.2 Combine like terms: 0 + 16.2 = 16.2 -3x + x2 = 16.2 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 = 16.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 16.2 + 2.25 Combine like terms: 16.2 + 2.25 = 18.45 2.25 + -3x + x2 = 18.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 18.45 Calculate the square root of the right side: 4.295346319 Break this problem into two subproblems by setting (x + -1.5) equal to 4.295346319 and -4.295346319.Subproblem 1
x + -1.5 = 4.295346319 Simplifying x + -1.5 = 4.295346319 Reorder the terms: -1.5 + x = 4.295346319 Solving -1.5 + x = 4.295346319 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 = 4.295346319 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.295346319 + 1.5 x = 4.295346319 + 1.5 Combine like terms: 4.295346319 + 1.5 = 5.795346319 x = 5.795346319 Simplifying x = 5.795346319Subproblem 2
x + -1.5 = -4.295346319 Simplifying x + -1.5 = -4.295346319 Reorder the terms: -1.5 + x = -4.295346319 Solving -1.5 + x = -4.295346319 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 = -4.295346319 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.295346319 + 1.5 x = -4.295346319 + 1.5 Combine like terms: -4.295346319 + 1.5 = -2.795346319 x = -2.795346319 Simplifying x = -2.795346319Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.795346319, -2.795346319}
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