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Simplifying 3x2 + 15x + -65 = 0 Reorder the terms: -65 + 15x + 3x2 = 0 Solving -65 + 15x + 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'. -21.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '21.66666667' to each side of the equation. -21.66666667 + 5x + 21.66666667 + x2 = 0 + 21.66666667 Reorder the terms: -21.66666667 + 21.66666667 + 5x + x2 = 0 + 21.66666667 Combine like terms: -21.66666667 + 21.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + 21.66666667 5x + x2 = 0 + 21.66666667 Combine like terms: 0 + 21.66666667 = 21.66666667 5x + x2 = 21.66666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 21.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 21.66666667 + 6.25 Combine like terms: 21.66666667 + 6.25 = 27.91666667 6.25 + 5x + x2 = 27.91666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 27.91666667 Calculate the square root of the right side: 5.283622495 Break this problem into two subproblems by setting (x + 2.5) equal to 5.283622495 and -5.283622495.Subproblem 1
x + 2.5 = 5.283622495 Simplifying x + 2.5 = 5.283622495 Reorder the terms: 2.5 + x = 5.283622495 Solving 2.5 + x = 5.283622495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.283622495 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.283622495 + -2.5 x = 5.283622495 + -2.5 Combine like terms: 5.283622495 + -2.5 = 2.783622495 x = 2.783622495 Simplifying x = 2.783622495Subproblem 2
x + 2.5 = -5.283622495 Simplifying x + 2.5 = -5.283622495 Reorder the terms: 2.5 + x = -5.283622495 Solving 2.5 + x = -5.283622495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.283622495 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.283622495 + -2.5 x = -5.283622495 + -2.5 Combine like terms: -5.283622495 + -2.5 = -7.783622495 x = -7.783622495 Simplifying x = -7.783622495Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.783622495, -7.783622495}
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