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Simplifying 4x2 + 7x + -2 = 13x + 3x2 + 33 Reorder the terms: -2 + 7x + 4x2 = 13x + 3x2 + 33 Reorder the terms: -2 + 7x + 4x2 = 33 + 13x + 3x2 Solving -2 + 7x + 4x2 = 33 + 13x + 3x2 Solving for variable 'x'. Reorder the terms: -2 + -33 + 7x + -13x + 4x2 + -3x2 = 33 + 13x + 3x2 + -33 + -13x + -3x2 Combine like terms: -2 + -33 = -35 -35 + 7x + -13x + 4x2 + -3x2 = 33 + 13x + 3x2 + -33 + -13x + -3x2 Combine like terms: 7x + -13x = -6x -35 + -6x + 4x2 + -3x2 = 33 + 13x + 3x2 + -33 + -13x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -35 + -6x + 1x2 = 33 + 13x + 3x2 + -33 + -13x + -3x2 Reorder the terms: -35 + -6x + 1x2 = 33 + -33 + 13x + -13x + 3x2 + -3x2 Combine like terms: 33 + -33 = 0 -35 + -6x + 1x2 = 0 + 13x + -13x + 3x2 + -3x2 -35 + -6x + 1x2 = 13x + -13x + 3x2 + -3x2 Combine like terms: 13x + -13x = 0 -35 + -6x + 1x2 = 0 + 3x2 + -3x2 -35 + -6x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -35 + -6x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -6x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -6x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -6x + x2 = 0 + 35 -6x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -6x + x2 = 35 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 = 35 + 9 Reorder the terms: 9 + -6x + x2 = 35 + 9 Combine like terms: 35 + 9 = 44 9 + -6x + x2 = 44 Factor a perfect square on the left side: (x + -3)(x + -3) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -3) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -3 = 6.633249581 Simplifying x + -3 = 6.633249581 Reorder the terms: -3 + x = 6.633249581 Solving -3 + x = 6.633249581 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 = 6.633249581 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.633249581 + 3 x = 6.633249581 + 3 Combine like terms: 6.633249581 + 3 = 9.633249581 x = 9.633249581 Simplifying x = 9.633249581Subproblem 2
x + -3 = -6.633249581 Simplifying x + -3 = -6.633249581 Reorder the terms: -3 + x = -6.633249581 Solving -3 + x = -6.633249581 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 = -6.633249581 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.633249581 + 3 x = -6.633249581 + 3 Combine like terms: -6.633249581 + 3 = -3.633249581 x = -3.633249581 Simplifying x = -3.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.633249581, -3.633249581}
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