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Simplifying (x + -7 + 5) * x + -7 = 36 Reorder the terms: (-7 + 5 + x) * x + -7 = 36 Combine like terms: -7 + 5 = -2 (-2 + x) * x + -7 = 36 Reorder the terms for easier multiplication: x(-2 + x) + -7 = 36 (-2 * x + x * x) + -7 = 36 (-2x + x2) + -7 = 36 Reorder the terms: -7 + -2x + x2 = 36 Solving -7 + -2x + x2 = 36 Solving for variable 'x'. Reorder the terms: -7 + -36 + -2x + x2 = 36 + -36 Combine like terms: -7 + -36 = -43 -43 + -2x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -43 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -2x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -2x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -2x + x2 = 0 + 43 -2x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -2x + x2 = 43 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 43 + 1 Reorder the terms: 1 + -2x + x2 = 43 + 1 Combine like terms: 43 + 1 = 44 1 + -2x + x2 = 44 Factor a perfect square on the left side: (x + -1)(x + -1) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -1) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -1 = 6.633249581 Simplifying x + -1 = 6.633249581 Reorder the terms: -1 + x = 6.633249581 Solving -1 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.633249581 + 1 x = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 x = 7.633249581 Simplifying x = 7.633249581Subproblem 2
x + -1 = -6.633249581 Simplifying x + -1 = -6.633249581 Reorder the terms: -1 + x = -6.633249581 Solving -1 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.633249581 + 1 x = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 x = -5.633249581 Simplifying x = -5.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.633249581, -5.633249581}
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