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Simplifying -0.1x2 + 30x + -1890 = 0 Reorder the terms: -1890 + 30x + -0.1x2 = 0 Solving -1890 + 30x + -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'. 18900 + -300x + x2 = 0 Move the constant term to the right: Add '-18900' to each side of the equation. 18900 + -300x + -18900 + x2 = 0 + -18900 Reorder the terms: 18900 + -18900 + -300x + x2 = 0 + -18900 Combine like terms: 18900 + -18900 = 0 0 + -300x + x2 = 0 + -18900 -300x + x2 = 0 + -18900 Combine like terms: 0 + -18900 = -18900 -300x + x2 = -18900 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 = -18900 + 22500 Reorder the terms: 22500 + -300x + x2 = -18900 + 22500 Combine like terms: -18900 + 22500 = 3600 22500 + -300x + x2 = 3600 Factor a perfect square on the left side: (x + -150)(x + -150) = 3600 Calculate the square root of the right side: 60 Break this problem into two subproblems by setting (x + -150) equal to 60 and -60.Subproblem 1
x + -150 = 60 Simplifying x + -150 = 60 Reorder the terms: -150 + x = 60 Solving -150 + x = 60 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 = 60 + 150 Combine like terms: -150 + 150 = 0 0 + x = 60 + 150 x = 60 + 150 Combine like terms: 60 + 150 = 210 x = 210 Simplifying x = 210Subproblem 2
x + -150 = -60 Simplifying x + -150 = -60 Reorder the terms: -150 + x = -60 Solving -150 + x = -60 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 = -60 + 150 Combine like terms: -150 + 150 = 0 0 + x = -60 + 150 x = -60 + 150 Combine like terms: -60 + 150 = 90 x = 90 Simplifying x = 90Solution
The solution to the problem is based on the solutions from the subproblems. x = {210, 90}
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