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Simplifying (x + 0) = 36 + -12x + -5x2 Reorder the terms: (0 + x) = 36 + -12x + -5x2 Remove the zero: (x) = 36 + -12x + -5x2 x = 36 + -12x + -5x2 Solving x = 36 + -12x + -5x2 Solving for variable 'x'. Reorder the terms: -36 + x + 12x + 5x2 = 36 + -12x + -5x2 + -36 + 12x + 5x2 Combine like terms: x + 12x = 13x -36 + 13x + 5x2 = 36 + -12x + -5x2 + -36 + 12x + 5x2 Reorder the terms: -36 + 13x + 5x2 = 36 + -36 + -12x + 12x + -5x2 + 5x2 Combine like terms: 36 + -36 = 0 -36 + 13x + 5x2 = 0 + -12x + 12x + -5x2 + 5x2 -36 + 13x + 5x2 = -12x + 12x + -5x2 + 5x2 Combine like terms: -12x + 12x = 0 -36 + 13x + 5x2 = 0 + -5x2 + 5x2 -36 + 13x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -36 + 13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 2.6x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 2.6x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 2.6x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 2.6x + x2 = 0 + 7.2 2.6x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 2.6x + x2 = 7.2 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 7.2 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 7.2 + 1.69 Combine like terms: 7.2 + 1.69 = 8.89 1.69 + 2.6x + x2 = 8.89 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 8.89 Calculate the square root of the right side: 2.981610303 Break this problem into two subproblems by setting (x + 1.3) equal to 2.981610303 and -2.981610303.Subproblem 1
x + 1.3 = 2.981610303 Simplifying x + 1.3 = 2.981610303 Reorder the terms: 1.3 + x = 2.981610303 Solving 1.3 + x = 2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.981610303 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.981610303 + -1.3 x = 2.981610303 + -1.3 Combine like terms: 2.981610303 + -1.3 = 1.681610303 x = 1.681610303 Simplifying x = 1.681610303Subproblem 2
x + 1.3 = -2.981610303 Simplifying x + 1.3 = -2.981610303 Reorder the terms: 1.3 + x = -2.981610303 Solving 1.3 + x = -2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.981610303 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.981610303 + -1.3 x = -2.981610303 + -1.3 Combine like terms: -2.981610303 + -1.3 = -4.281610303 x = -4.281610303 Simplifying x = -4.281610303Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.681610303, -4.281610303}
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