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Simplifying -1x2 + 4x = -39 Reorder the terms: 4x + -1x2 = -39 Solving 4x + -1x2 = -39 Solving for variable 'x'. Reorder the terms: 39 + 4x + -1x2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + -4x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -4x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -4x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -4x + x2 = 0 + 39 -4x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -4x + x2 = 39 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 39 + 4 Reorder the terms: 4 + -4x + x2 = 39 + 4 Combine like terms: 39 + 4 = 43 4 + -4x + x2 = 43 Factor a perfect square on the left side: (x + -2)(x + -2) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -2) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -2 = 6.557438524 Simplifying x + -2 = 6.557438524 Reorder the terms: -2 + x = 6.557438524 Solving -2 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.557438524 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.557438524 + 2 x = 6.557438524 + 2 Combine like terms: 6.557438524 + 2 = 8.557438524 x = 8.557438524 Simplifying x = 8.557438524Subproblem 2
x + -2 = -6.557438524 Simplifying x + -2 = -6.557438524 Reorder the terms: -2 + x = -6.557438524 Solving -2 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.557438524 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.557438524 + 2 x = -6.557438524 + 2 Combine like terms: -6.557438524 + 2 = -4.557438524 x = -4.557438524 Simplifying x = -4.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.557438524, -4.557438524}
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