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Simplifying 4x2 + 36x + 5 = 0 Reorder the terms: 5 + 36x + 4x2 = 0 Solving 5 + 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'. 1.25 + 9x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 9x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 9x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 9x + x2 = 0 + -1.25 9x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 9x + x2 = -1.25 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 = -1.25 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -1.25 + 20.25 Combine like terms: -1.25 + 20.25 = 19 20.25 + 9x + x2 = 19 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 4.5) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 4.5 = 4.358898944 Simplifying x + 4.5 = 4.358898944 Reorder the terms: 4.5 + x = 4.358898944 Solving 4.5 + x = 4.358898944 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 = 4.358898944 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.358898944 + -4.5 x = 4.358898944 + -4.5 Combine like terms: 4.358898944 + -4.5 = -0.141101056 x = -0.141101056 Simplifying x = -0.141101056Subproblem 2
x + 4.5 = -4.358898944 Simplifying x + 4.5 = -4.358898944 Reorder the terms: 4.5 + x = -4.358898944 Solving 4.5 + x = -4.358898944 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 = -4.358898944 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.358898944 + -4.5 x = -4.358898944 + -4.5 Combine like terms: -4.358898944 + -4.5 = -8.858898944 x = -8.858898944 Simplifying x = -8.858898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.141101056, -8.858898944}
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