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Simplifying 4x2 + -29x = 3x2 + -5x + -9 Reorder the terms: -29x + 4x2 = 3x2 + -5x + -9 Reorder the terms: -29x + 4x2 = -9 + -5x + 3x2 Solving -29x + 4x2 = -9 + -5x + 3x2 Solving for variable 'x'. Reorder the terms: 9 + -29x + 5x + 4x2 + -3x2 = -9 + -5x + 3x2 + 9 + 5x + -3x2 Combine like terms: -29x + 5x = -24x 9 + -24x + 4x2 + -3x2 = -9 + -5x + 3x2 + 9 + 5x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 9 + -24x + 1x2 = -9 + -5x + 3x2 + 9 + 5x + -3x2 Reorder the terms: 9 + -24x + 1x2 = -9 + 9 + -5x + 5x + 3x2 + -3x2 Combine like terms: -9 + 9 = 0 9 + -24x + 1x2 = 0 + -5x + 5x + 3x2 + -3x2 9 + -24x + 1x2 = -5x + 5x + 3x2 + -3x2 Combine like terms: -5x + 5x = 0 9 + -24x + 1x2 = 0 + 3x2 + -3x2 9 + -24x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 9 + -24x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -24x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -24x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -24x + x2 = 0 + -9 -24x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -24x + x2 = -9 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -9 + 144 Reorder the terms: 144 + -24x + x2 = -9 + 144 Combine like terms: -9 + 144 = 135 144 + -24x + x2 = 135 Factor a perfect square on the left side: (x + -12)(x + -12) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -12) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -12 = 11.618950039 Simplifying x + -12 = 11.618950039 Reorder the terms: -12 + x = 11.618950039 Solving -12 + x = 11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.618950039 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.618950039 + 12 x = 11.618950039 + 12 Combine like terms: 11.618950039 + 12 = 23.618950039 x = 23.618950039 Simplifying x = 23.618950039Subproblem 2
x + -12 = -11.618950039 Simplifying x + -12 = -11.618950039 Reorder the terms: -12 + x = -11.618950039 Solving -12 + x = -11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.618950039 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.618950039 + 12 x = -11.618950039 + 12 Combine like terms: -11.618950039 + 12 = 0.381049961 x = 0.381049961 Simplifying x = 0.381049961Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.618950039, 0.381049961}
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