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Simplifying 4x2 + 36x + 25 = 0 Reorder the terms: 25 + 36x + 4x2 = 0 Solving 25 + 36x + 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'. 6.25 + 9x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 9x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 9x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 9x + x2 = 0 + -6.25 9x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 9x + x2 = -6.25 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -6.25 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -6.25 + 20.25 Combine like terms: -6.25 + 20.25 = 14 20.25 + 9x + x2 = 14 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 4.5) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 4.5 = 3.741657387 Simplifying x + 4.5 = 3.741657387 Reorder the terms: 4.5 + x = 3.741657387 Solving 4.5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.741657387 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.741657387 + -4.5 x = 3.741657387 + -4.5 Combine like terms: 3.741657387 + -4.5 = -0.758342613 x = -0.758342613 Simplifying x = -0.758342613Subproblem 2
x + 4.5 = -3.741657387 Simplifying x + 4.5 = -3.741657387 Reorder the terms: 4.5 + x = -3.741657387 Solving 4.5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.741657387 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.741657387 + -4.5 x = -3.741657387 + -4.5 Combine like terms: -3.741657387 + -4.5 = -8.241657387 x = -8.241657387 Simplifying x = -8.241657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.758342613, -8.241657387}
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