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Simplifying (6x2 + -4x + -29) + (4x2 + 9x) = 0 Reorder the terms: (-29 + -4x + 6x2) + (4x2 + 9x) = 0 Remove parenthesis around (-29 + -4x + 6x2) -29 + -4x + 6x2 + (4x2 + 9x) = 0 Reorder the terms: -29 + -4x + 6x2 + (9x + 4x2) = 0 Remove parenthesis around (9x + 4x2) -29 + -4x + 6x2 + 9x + 4x2 = 0 Reorder the terms: -29 + -4x + 9x + 6x2 + 4x2 = 0 Combine like terms: -4x + 9x = 5x -29 + 5x + 6x2 + 4x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 -29 + 5x + 10x2 = 0 Solving -29 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.9 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '2.9' to each side of the equation. -2.9 + 0.5x + 2.9 + x2 = 0.0 + 2.9 Reorder the terms: -2.9 + 2.9 + 0.5x + x2 = 0.0 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + 0.5x + x2 = 0.0 + 2.9 0.5x + x2 = 0.0 + 2.9 Combine like terms: 0.0 + 2.9 = 2.9 0.5x + x2 = 2.9 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.9 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.9 + 0.0625 Combine like terms: 2.9 + 0.0625 = 2.9625 0.0625 + 0.5x + x2 = 2.9625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.9625 Calculate the square root of the right side: 1.721191448 Break this problem into two subproblems by setting (x + 0.25) equal to 1.721191448 and -1.721191448.Subproblem 1
x + 0.25 = 1.721191448 Simplifying x + 0.25 = 1.721191448 Reorder the terms: 0.25 + x = 1.721191448 Solving 0.25 + x = 1.721191448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.721191448 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.721191448 + -0.25 x = 1.721191448 + -0.25 Combine like terms: 1.721191448 + -0.25 = 1.471191448 x = 1.471191448 Simplifying x = 1.471191448Subproblem 2
x + 0.25 = -1.721191448 Simplifying x + 0.25 = -1.721191448 Reorder the terms: 0.25 + x = -1.721191448 Solving 0.25 + x = -1.721191448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.721191448 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.721191448 + -0.25 x = -1.721191448 + -0.25 Combine like terms: -1.721191448 + -0.25 = -1.971191448 x = -1.971191448 Simplifying x = -1.971191448Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.471191448, -1.971191448}
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