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Simplifying x2 + -8x + -10x = -4x + 2 Reorder the terms: -8x + -10x + x2 = -4x + 2 Combine like terms: -8x + -10x = -18x -18x + x2 = -4x + 2 Reorder the terms: -18x + x2 = 2 + -4x Solving -18x + x2 = 2 + -4x Solving for variable 'x'. Reorder the terms: -2 + -18x + 4x + x2 = 2 + -4x + -2 + 4x Combine like terms: -18x + 4x = -14x -2 + -14x + x2 = 2 + -4x + -2 + 4x Reorder the terms: -2 + -14x + x2 = 2 + -2 + -4x + 4x Combine like terms: 2 + -2 = 0 -2 + -14x + x2 = 0 + -4x + 4x -2 + -14x + x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -2 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -14x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -14x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -14x + x2 = 0 + 2 -14x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -14x + x2 = 2 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 2 + 49 Reorder the terms: 49 + -14x + x2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + -14x + x2 = 51 Factor a perfect square on the left side: (x + -7)(x + -7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -7) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -7 = 7.141428429 Simplifying x + -7 = 7.141428429 Reorder the terms: -7 + x = 7.141428429 Solving -7 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.141428429 + 7 x = 7.141428429 + 7 Combine like terms: 7.141428429 + 7 = 14.141428429 x = 14.141428429 Simplifying x = 14.141428429Subproblem 2
x + -7 = -7.141428429 Simplifying x + -7 = -7.141428429 Reorder the terms: -7 + x = -7.141428429 Solving -7 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.141428429 + 7 x = -7.141428429 + 7 Combine like terms: -7.141428429 + 7 = -0.141428429 x = -0.141428429 Simplifying x = -0.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.141428429, -0.141428429}
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