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Simplifying 4x2 + 20x = 29 Reorder the terms: 20x + 4x2 = 29 Solving 20x + 4x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 20x + 4x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + 5x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 5x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 5x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 5x + x2 = 0 + 7.25 5x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 5x + x2 = 7.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 7.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 7.25 + 6.25 Combine like terms: 7.25 + 6.25 = 13.5 6.25 + 5x + x2 = 13.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + 2.5) equal to 3.674234614 and -3.674234614.Subproblem 1
x + 2.5 = 3.674234614 Simplifying x + 2.5 = 3.674234614 Reorder the terms: 2.5 + x = 3.674234614 Solving 2.5 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.674234614 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.674234614 + -2.5 x = 3.674234614 + -2.5 Combine like terms: 3.674234614 + -2.5 = 1.174234614 x = 1.174234614 Simplifying x = 1.174234614Subproblem 2
x + 2.5 = -3.674234614 Simplifying x + 2.5 = -3.674234614 Reorder the terms: 2.5 + x = -3.674234614 Solving 2.5 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.674234614 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.674234614 + -2.5 x = -3.674234614 + -2.5 Combine like terms: -3.674234614 + -2.5 = -6.174234614 x = -6.174234614 Simplifying x = -6.174234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.174234614, -6.174234614}
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