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Simplifying (3x2 + 5x) + (x2 + -29) = 0 Reorder the terms: (5x + 3x2) + (x2 + -29) = 0 Remove parenthesis around (5x + 3x2) 5x + 3x2 + (x2 + -29) = 0 Reorder the terms: 5x + 3x2 + (-29 + x2) = 0 Remove parenthesis around (-29 + x2) 5x + 3x2 + -29 + x2 = 0 Reorder the terms: -29 + 5x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 -29 + 5x + 4x2 = 0 Solving -29 + 5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 1.25x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 1.25x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 1.25x + x2 = 0 + 7.25 1.25x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 1.25x + x2 = 7.25 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 7.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 7.25 + 0.390625 Combine like terms: 7.25 + 0.390625 = 7.640625 0.390625 + 1.25x + x2 = 7.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting (x + 0.625) equal to 2.764168048 and -2.764168048.Subproblem 1
x + 0.625 = 2.764168048 Simplifying x + 0.625 = 2.764168048 Reorder the terms: 0.625 + x = 2.764168048 Solving 0.625 + x = 2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.764168048 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.764168048 + -0.625 x = 2.764168048 + -0.625 Combine like terms: 2.764168048 + -0.625 = 2.139168048 x = 2.139168048 Simplifying x = 2.139168048Subproblem 2
x + 0.625 = -2.764168048 Simplifying x + 0.625 = -2.764168048 Reorder the terms: 0.625 + x = -2.764168048 Solving 0.625 + x = -2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.764168048 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.764168048 + -0.625 x = -2.764168048 + -0.625 Combine like terms: -2.764168048 + -0.625 = -3.389168048 x = -3.389168048 Simplifying x = -3.389168048Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.139168048, -3.389168048}
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