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Simplifying 0 = 0.1x2 + -30x + 1400 Reorder the terms: 0 = 1400 + -30x + 0.1x2 Solving 0 = 1400 + -30x + 0.1x2 Solving for variable 'x'. Combine like terms: 0 + -1400 = -1400 -1400 + 30x + -0.1x2 = 1400 + -30x + 0.1x2 + -1400 + 30x + -0.1x2 Reorder the terms: -1400 + 30x + -0.1x2 = 1400 + -1400 + -30x + 30x + 0.1x2 + -0.1x2 Combine like terms: 1400 + -1400 = 0 -1400 + 30x + -0.1x2 = 0 + -30x + 30x + 0.1x2 + -0.1x2 -1400 + 30x + -0.1x2 = -30x + 30x + 0.1x2 + -0.1x2 Combine like terms: -30x + 30x = 0 -1400 + 30x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -1400 + 30x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -1400 + 30x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 14000 + -300x + x2 = 0 Move the constant term to the right: Add '-14000' to each side of the equation. 14000 + -300x + -14000 + x2 = 0 + -14000 Reorder the terms: 14000 + -14000 + -300x + x2 = 0 + -14000 Combine like terms: 14000 + -14000 = 0 0 + -300x + x2 = 0 + -14000 -300x + x2 = 0 + -14000 Combine like terms: 0 + -14000 = -14000 -300x + x2 = -14000 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -14000 + 22500 Reorder the terms: 22500 + -300x + x2 = -14000 + 22500 Combine like terms: -14000 + 22500 = 8500 22500 + -300x + x2 = 8500 Factor a perfect square on the left side: (x + -150)(x + -150) = 8500 Calculate the square root of the right side: 92.195444573 Break this problem into two subproblems by setting (x + -150) equal to 92.195444573 and -92.195444573.Subproblem 1
x + -150 = 92.195444573 Simplifying x + -150 = 92.195444573 Reorder the terms: -150 + x = 92.195444573 Solving -150 + x = 92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 92.195444573 + 150 Combine like terms: -150 + 150 = 0 0 + x = 92.195444573 + 150 x = 92.195444573 + 150 Combine like terms: 92.195444573 + 150 = 242.195444573 x = 242.195444573 Simplifying x = 242.195444573Subproblem 2
x + -150 = -92.195444573 Simplifying x + -150 = -92.195444573 Reorder the terms: -150 + x = -92.195444573 Solving -150 + x = -92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -92.195444573 + 150 Combine like terms: -150 + 150 = 0 0 + x = -92.195444573 + 150 x = -92.195444573 + 150 Combine like terms: -92.195444573 + 150 = 57.804555427 x = 57.804555427 Simplifying x = 57.804555427Solution
The solution to the problem is based on the solutions from the subproblems. x = {242.195444573, 57.804555427}
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