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Simplifying 0.1x2 + 5x + -140 = 0 Reorder the terms: -140 + 5x + 0.1x2 = 0 Solving -140 + 5x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -1400 + 50x + x2 = 0 Move the constant term to the right: Add '1400' to each side of the equation. -1400 + 50x + 1400 + x2 = 0 + 1400 Reorder the terms: -1400 + 1400 + 50x + x2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + 50x + x2 = 0 + 1400 50x + x2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 50x + x2 = 1400 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 1400 + 625 Reorder the terms: 625 + 50x + x2 = 1400 + 625 Combine like terms: 1400 + 625 = 2025 625 + 50x + x2 = 2025 Factor a perfect square on the left side: (x + 25)(x + 25) = 2025 Calculate the square root of the right side: 45 Break this problem into two subproblems by setting (x + 25) equal to 45 and -45.Subproblem 1
x + 25 = 45 Simplifying x + 25 = 45 Reorder the terms: 25 + x = 45 Solving 25 + x = 45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 45 + -25 Combine like terms: 25 + -25 = 0 0 + x = 45 + -25 x = 45 + -25 Combine like terms: 45 + -25 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 25 = -45 Simplifying x + 25 = -45 Reorder the terms: 25 + x = -45 Solving 25 + x = -45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -45 + -25 Combine like terms: 25 + -25 = 0 0 + x = -45 + -25 x = -45 + -25 Combine like terms: -45 + -25 = -70 x = -70 Simplifying x = -70Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -70}
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