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Simplifying -4(x2 + -6x + -36) = 39 Reorder the terms: -4(-36 + -6x + x2) = 39 (-36 * -4 + -6x * -4 + x2 * -4) = 39 (144 + 24x + -4x2) = 39 Solving 144 + 24x + -4x2 = 39 Solving for variable 'x'. Reorder the terms: 144 + -39 + 24x + -4x2 = 39 + -39 Combine like terms: 144 + -39 = 105 105 + 24x + -4x2 = 39 + -39 Combine like terms: 39 + -39 = 0 105 + 24x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -26.25 + -6x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + -6x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + -6x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + -6x + x2 = 0 + 26.25 -6x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 -6x + x2 = 26.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 26.25 + 9 Reorder the terms: 9 + -6x + x2 = 26.25 + 9 Combine like terms: 26.25 + 9 = 35.25 9 + -6x + x2 = 35.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -3) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -3 = 5.937171044 Simplifying x + -3 = 5.937171044 Reorder the terms: -3 + x = 5.937171044 Solving -3 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.937171044 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.937171044 + 3 x = 5.937171044 + 3 Combine like terms: 5.937171044 + 3 = 8.937171044 x = 8.937171044 Simplifying x = 8.937171044Subproblem 2
x + -3 = -5.937171044 Simplifying x + -3 = -5.937171044 Reorder the terms: -3 + x = -5.937171044 Solving -3 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.937171044 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.937171044 + 3 x = -5.937171044 + 3 Combine like terms: -5.937171044 + 3 = -2.937171044 x = -2.937171044 Simplifying x = -2.937171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.937171044, -2.937171044}
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