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Simplifying 0.003x2 + 3.9x + 150 = 0 Reorder the terms: 150 + 3.9x + 0.003x2 = 0 Solving 150 + 3.9x + 0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. 50000 + 1300x + x2 = 0 Move the constant term to the right: Add '-50000' to each side of the equation. 50000 + 1300x + -50000 + x2 = 0 + -50000 Reorder the terms: 50000 + -50000 + 1300x + x2 = 0 + -50000 Combine like terms: 50000 + -50000 = 0 0 + 1300x + x2 = 0 + -50000 1300x + x2 = 0 + -50000 Combine like terms: 0 + -50000 = -50000 1300x + x2 = -50000 The x term is 1300x. Take half its coefficient (650). Square it (422500) and add it to both sides. Add '422500' to each side of the equation. 1300x + 422500 + x2 = -50000 + 422500 Reorder the terms: 422500 + 1300x + x2 = -50000 + 422500 Combine like terms: -50000 + 422500 = 372500 422500 + 1300x + x2 = 372500 Factor a perfect square on the left side: (x + 650)(x + 650) = 372500 Calculate the square root of the right side: 610.327780787 Break this problem into two subproblems by setting (x + 650) equal to 610.327780787 and -610.327780787.Subproblem 1
x + 650 = 610.327780787 Simplifying x + 650 = 610.327780787 Reorder the terms: 650 + x = 610.327780787 Solving 650 + x = 610.327780787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-650' to each side of the equation. 650 + -650 + x = 610.327780787 + -650 Combine like terms: 650 + -650 = 0 0 + x = 610.327780787 + -650 x = 610.327780787 + -650 Combine like terms: 610.327780787 + -650 = -39.672219213 x = -39.672219213 Simplifying x = -39.672219213Subproblem 2
x + 650 = -610.327780787 Simplifying x + 650 = -610.327780787 Reorder the terms: 650 + x = -610.327780787 Solving 650 + x = -610.327780787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-650' to each side of the equation. 650 + -650 + x = -610.327780787 + -650 Combine like terms: 650 + -650 = 0 0 + x = -610.327780787 + -650 x = -610.327780787 + -650 Combine like terms: -610.327780787 + -650 = -1260.327780787 x = -1260.327780787 Simplifying x = -1260.327780787Solution
The solution to the problem is based on the solutions from the subproblems. x = {-39.672219213, -1260.327780787}
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