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Simplifying 2x2 + 10x + -6x + -30 = 4 + 8x + x2 Reorder the terms: -30 + 10x + -6x + 2x2 = 4 + 8x + x2 Combine like terms: 10x + -6x = 4x -30 + 4x + 2x2 = 4 + 8x + x2 Solving -30 + 4x + 2x2 = 4 + 8x + x2 Solving for variable 'x'. Reorder the terms: -30 + -4 + 4x + -8x + 2x2 + -1x2 = 4 + 8x + x2 + -4 + -8x + -1x2 Combine like terms: -30 + -4 = -34 -34 + 4x + -8x + 2x2 + -1x2 = 4 + 8x + x2 + -4 + -8x + -1x2 Combine like terms: 4x + -8x = -4x -34 + -4x + 2x2 + -1x2 = 4 + 8x + x2 + -4 + -8x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -34 + -4x + 1x2 = 4 + 8x + x2 + -4 + -8x + -1x2 Reorder the terms: -34 + -4x + 1x2 = 4 + -4 + 8x + -8x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -34 + -4x + 1x2 = 0 + 8x + -8x + x2 + -1x2 -34 + -4x + 1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -34 + -4x + 1x2 = 0 + x2 + -1x2 -34 + -4x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -34 + -4x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -4x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -4x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -4x + x2 = 0 + 34 -4x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -4x + x2 = 34 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 = 34 + 4 Reorder the terms: 4 + -4x + x2 = 34 + 4 Combine like terms: 34 + 4 = 38 4 + -4x + x2 = 38 Factor a perfect square on the left side: (x + -2)(x + -2) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -2) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -2 = 6.164414003 Simplifying x + -2 = 6.164414003 Reorder the terms: -2 + x = 6.164414003 Solving -2 + x = 6.164414003 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 = 6.164414003 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.164414003 + 2 x = 6.164414003 + 2 Combine like terms: 6.164414003 + 2 = 8.164414003 x = 8.164414003 Simplifying x = 8.164414003Subproblem 2
x + -2 = -6.164414003 Simplifying x + -2 = -6.164414003 Reorder the terms: -2 + x = -6.164414003 Solving -2 + x = -6.164414003 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 = -6.164414003 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.164414003 + 2 x = -6.164414003 + 2 Combine like terms: -6.164414003 + 2 = -4.164414003 x = -4.164414003 Simplifying x = -4.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.164414003, -4.164414003}
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