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Simplifying 0.4x2 + 36x + 56 = 0 Reorder the terms: 56 + 36x + 0.4x2 = 0 Solving 56 + 36x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 140 + 90x + x2 = 0 Move the constant term to the right: Add '-140' to each side of the equation. 140 + 90x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + 90x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + 90x + x2 = 0 + -140 90x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 90x + x2 = -140 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = -140 + 2025 Reorder the terms: 2025 + 90x + x2 = -140 + 2025 Combine like terms: -140 + 2025 = 1885 2025 + 90x + x2 = 1885 Factor a perfect square on the left side: (x + 45)(x + 45) = 1885 Calculate the square root of the right side: 43.416586692 Break this problem into two subproblems by setting (x + 45) equal to 43.416586692 and -43.416586692.Subproblem 1
x + 45 = 43.416586692 Simplifying x + 45 = 43.416586692 Reorder the terms: 45 + x = 43.416586692 Solving 45 + x = 43.416586692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 43.416586692 + -45 Combine like terms: 45 + -45 = 0 0 + x = 43.416586692 + -45 x = 43.416586692 + -45 Combine like terms: 43.416586692 + -45 = -1.583413308 x = -1.583413308 Simplifying x = -1.583413308Subproblem 2
x + 45 = -43.416586692 Simplifying x + 45 = -43.416586692 Reorder the terms: 45 + x = -43.416586692 Solving 45 + x = -43.416586692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -43.416586692 + -45 Combine like terms: 45 + -45 = 0 0 + x = -43.416586692 + -45 x = -43.416586692 + -45 Combine like terms: -43.416586692 + -45 = -88.416586692 x = -88.416586692 Simplifying x = -88.416586692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.583413308, -88.416586692}
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