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Simplifying 4x2 + 29x + 13 = -9x + 4 Reorder the terms: 13 + 29x + 4x2 = -9x + 4 Reorder the terms: 13 + 29x + 4x2 = 4 + -9x Solving 13 + 29x + 4x2 = 4 + -9x Solving for variable 'x'. Reorder the terms: 13 + -4 + 29x + 9x + 4x2 = 4 + -9x + -4 + 9x Combine like terms: 13 + -4 = 9 9 + 29x + 9x + 4x2 = 4 + -9x + -4 + 9x Combine like terms: 29x + 9x = 38x 9 + 38x + 4x2 = 4 + -9x + -4 + 9x Reorder the terms: 9 + 38x + 4x2 = 4 + -4 + -9x + 9x Combine like terms: 4 + -4 = 0 9 + 38x + 4x2 = 0 + -9x + 9x 9 + 38x + 4x2 = -9x + 9x Combine like terms: -9x + 9x = 0 9 + 38x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 9.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 9.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 9.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 9.5x + x2 = 0 + -2.25 9.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 9.5x + x2 = -2.25 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -2.25 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -2.25 + 22.5625 Combine like terms: -2.25 + 22.5625 = 20.3125 22.5625 + 9.5x + x2 = 20.3125 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 20.3125 Calculate the square root of the right side: 4.506939094 Break this problem into two subproblems by setting (x + 4.75) equal to 4.506939094 and -4.506939094.Subproblem 1
x + 4.75 = 4.506939094 Simplifying x + 4.75 = 4.506939094 Reorder the terms: 4.75 + x = 4.506939094 Solving 4.75 + x = 4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 4.506939094 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.506939094 + -4.75 x = 4.506939094 + -4.75 Combine like terms: 4.506939094 + -4.75 = -0.243060906 x = -0.243060906 Simplifying x = -0.243060906Subproblem 2
x + 4.75 = -4.506939094 Simplifying x + 4.75 = -4.506939094 Reorder the terms: 4.75 + x = -4.506939094 Solving 4.75 + x = -4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -4.506939094 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.506939094 + -4.75 x = -4.506939094 + -4.75 Combine like terms: -4.506939094 + -4.75 = -9.256939094 x = -9.256939094 Simplifying x = -9.256939094Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.243060906, -9.256939094}
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