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Simplifying 5x2 + -29x = 4x2 + -7x + -8 Reorder the terms: -29x + 5x2 = 4x2 + -7x + -8 Reorder the terms: -29x + 5x2 = -8 + -7x + 4x2 Solving -29x + 5x2 = -8 + -7x + 4x2 Solving for variable 'x'. Reorder the terms: 8 + -29x + 7x + 5x2 + -4x2 = -8 + -7x + 4x2 + 8 + 7x + -4x2 Combine like terms: -29x + 7x = -22x 8 + -22x + 5x2 + -4x2 = -8 + -7x + 4x2 + 8 + 7x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 8 + -22x + 1x2 = -8 + -7x + 4x2 + 8 + 7x + -4x2 Reorder the terms: 8 + -22x + 1x2 = -8 + 8 + -7x + 7x + 4x2 + -4x2 Combine like terms: -8 + 8 = 0 8 + -22x + 1x2 = 0 + -7x + 7x + 4x2 + -4x2 8 + -22x + 1x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 8 + -22x + 1x2 = 0 + 4x2 + -4x2 8 + -22x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + -22x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -22x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -22x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -22x + x2 = 0 + -8 -22x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -22x + x2 = -8 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -8 + 121 Reorder the terms: 121 + -22x + x2 = -8 + 121 Combine like terms: -8 + 121 = 113 121 + -22x + x2 = 113 Factor a perfect square on the left side: (x + -11)(x + -11) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + -11) equal to 10.630145813 and -10.630145813.Subproblem 1
x + -11 = 10.630145813 Simplifying x + -11 = 10.630145813 Reorder the terms: -11 + x = 10.630145813 Solving -11 + x = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.630145813 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.630145813 + 11 x = 10.630145813 + 11 Combine like terms: 10.630145813 + 11 = 21.630145813 x = 21.630145813 Simplifying x = 21.630145813Subproblem 2
x + -11 = -10.630145813 Simplifying x + -11 = -10.630145813 Reorder the terms: -11 + x = -10.630145813 Solving -11 + x = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.630145813 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.630145813 + 11 x = -10.630145813 + 11 Combine like terms: -10.630145813 + 11 = 0.369854187 x = 0.369854187 Simplifying x = 0.369854187Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.630145813, 0.369854187}
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