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Simplifying -0.2x2 + 10x + 280 = 0 Reorder the terms: 280 + 10x + -0.2x2 = 0 Solving 280 + 10x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -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 = 70 x = 70 Simplifying x = 70Subproblem 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 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {70, -20}
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