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Simplifying 0.4x2 + -36x + 170 = 0 Reorder the terms: 170 + -36x + 0.4x2 = 0 Solving 170 + -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'. 425 + -90x + x2 = 0 Move the constant term to the right: Add '-425' to each side of the equation. 425 + -90x + -425 + x2 = 0 + -425 Reorder the terms: 425 + -425 + -90x + x2 = 0 + -425 Combine like terms: 425 + -425 = 0 0 + -90x + x2 = 0 + -425 -90x + x2 = 0 + -425 Combine like terms: 0 + -425 = -425 -90x + x2 = -425 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 = -425 + 2025 Reorder the terms: 2025 + -90x + x2 = -425 + 2025 Combine like terms: -425 + 2025 = 1600 2025 + -90x + x2 = 1600 Factor a perfect square on the left side: (x + -45)(x + -45) = 1600 Calculate the square root of the right side: 40 Break this problem into two subproblems by setting (x + -45) equal to 40 and -40.Subproblem 1
x + -45 = 40 Simplifying x + -45 = 40 Reorder the terms: -45 + x = 40 Solving -45 + x = 40 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 = 40 + 45 Combine like terms: -45 + 45 = 0 0 + x = 40 + 45 x = 40 + 45 Combine like terms: 40 + 45 = 85 x = 85 Simplifying x = 85Subproblem 2
x + -45 = -40 Simplifying x + -45 = -40 Reorder the terms: -45 + x = -40 Solving -45 + x = -40 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 = -40 + 45 Combine like terms: -45 + 45 = 0 0 + x = -40 + 45 x = -40 + 45 Combine like terms: -40 + 45 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {85, 5}
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