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Simplifying 20x + -1(2x + -1) * 2 = 29 + -2x(2x + 3) Reorder the terms: 20x + -1(-1 + 2x) * 2 = 29 + -2x(2x + 3) Reorder the terms for easier multiplication: 20x + -1 * 2(-1 + 2x) = 29 + -2x(2x + 3) Multiply -1 * 2 20x + -2(-1 + 2x) = 29 + -2x(2x + 3) 20x + (-1 * -2 + 2x * -2) = 29 + -2x(2x + 3) 20x + (2 + -4x) = 29 + -2x(2x + 3) Reorder the terms: 2 + 20x + -4x = 29 + -2x(2x + 3) Combine like terms: 20x + -4x = 16x 2 + 16x = 29 + -2x(2x + 3) Reorder the terms: 2 + 16x = 29 + -2x(3 + 2x) 2 + 16x = 29 + (3 * -2x + 2x * -2x) 2 + 16x = 29 + (-6x + -4x2) Solving 2 + 16x = 29 + -6x + -4x2 Solving for variable 'x'. Reorder the terms: 2 + -29 + 16x + 6x + 4x2 = 29 + -6x + -4x2 + -29 + 6x + 4x2 Combine like terms: 2 + -29 = -27 -27 + 16x + 6x + 4x2 = 29 + -6x + -4x2 + -29 + 6x + 4x2 Combine like terms: 16x + 6x = 22x -27 + 22x + 4x2 = 29 + -6x + -4x2 + -29 + 6x + 4x2 Reorder the terms: -27 + 22x + 4x2 = 29 + -29 + -6x + 6x + -4x2 + 4x2 Combine like terms: 29 + -29 = 0 -27 + 22x + 4x2 = 0 + -6x + 6x + -4x2 + 4x2 -27 + 22x + 4x2 = -6x + 6x + -4x2 + 4x2 Combine like terms: -6x + 6x = 0 -27 + 22x + 4x2 = 0 + -4x2 + 4x2 -27 + 22x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -27 + 22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 5.5x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 5.5x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 5.5x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 5.5x + x2 = 0 + 6.75 5.5x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 5.5x + x2 = 6.75 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 6.75 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 6.75 + 7.5625 Combine like terms: 6.75 + 7.5625 = 14.3125 7.5625 + 5.5x + x2 = 14.3125 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 14.3125 Calculate the square root of the right side: 3.783186488 Break this problem into two subproblems by setting (x + 2.75) equal to 3.783186488 and -3.783186488.Subproblem 1
x + 2.75 = 3.783186488 Simplifying x + 2.75 = 3.783186488 Reorder the terms: 2.75 + x = 3.783186488 Solving 2.75 + x = 3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.783186488 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.783186488 + -2.75 x = 3.783186488 + -2.75 Combine like terms: 3.783186488 + -2.75 = 1.033186488 x = 1.033186488 Simplifying x = 1.033186488Subproblem 2
x + 2.75 = -3.783186488 Simplifying x + 2.75 = -3.783186488 Reorder the terms: 2.75 + x = -3.783186488 Solving 2.75 + x = -3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.783186488 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.783186488 + -2.75 x = -3.783186488 + -2.75 Combine like terms: -3.783186488 + -2.75 = -6.533186488 x = -6.533186488 Simplifying x = -6.533186488Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.033186488, -6.533186488}
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