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Simplifying x2 + 6x + -40 = 48 Reorder the terms: -40 + 6x + x2 = 48 Solving -40 + 6x + x2 = 48 Solving for variable 'x'. Reorder the terms: -40 + -48 + 6x + x2 = 48 + -48 Combine like terms: -40 + -48 = -88 -88 + 6x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -88 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 6x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 6x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 6x + x2 = 0 + 88 6x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 6x + x2 = 88 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 = 88 + 9 Reorder the terms: 9 + 6x + x2 = 88 + 9 Combine like terms: 88 + 9 = 97 9 + 6x + x2 = 97 Factor a perfect square on the left side: (x + 3)(x + 3) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 3) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 3 = 9.848857802 Simplifying x + 3 = 9.848857802 Reorder the terms: 3 + x = 9.848857802 Solving 3 + x = 9.848857802 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 = 9.848857802 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.848857802 + -3 x = 9.848857802 + -3 Combine like terms: 9.848857802 + -3 = 6.848857802 x = 6.848857802 Simplifying x = 6.848857802Subproblem 2
x + 3 = -9.848857802 Simplifying x + 3 = -9.848857802 Reorder the terms: 3 + x = -9.848857802 Solving 3 + x = -9.848857802 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 = -9.848857802 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.848857802 + -3 x = -9.848857802 + -3 Combine like terms: -9.848857802 + -3 = -12.848857802 x = -12.848857802 Simplifying x = -12.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.848857802, -12.848857802}
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