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Simplifying 40 + -3x + 0.12x2 = 190 Solving 40 + -3x + 0.12x2 = 190 Solving for variable 'x'. Reorder the terms: 40 + -190 + -3x + 0.12x2 = 190 + -190 Combine like terms: 40 + -190 = -150 -150 + -3x + 0.12x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -150 + -3x + 0.12x2 = 0 Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. -1250 + -25x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + -25x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + -25x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + -25x + x2 = 0 + 1250 -25x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 -25x + x2 = 1250 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 1250 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 1250 + 156.25 Combine like terms: 1250 + 156.25 = 1406.25 156.25 + -25x + x2 = 1406.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 1406.25 Calculate the square root of the right side: 37.5 Break this problem into two subproblems by setting (x + -12.5) equal to 37.5 and -37.5.Subproblem 1
x + -12.5 = 37.5 Simplifying x + -12.5 = 37.5 Reorder the terms: -12.5 + x = 37.5 Solving -12.5 + x = 37.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 37.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 37.5 + 12.5 x = 37.5 + 12.5 Combine like terms: 37.5 + 12.5 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -12.5 = -37.5 Simplifying x + -12.5 = -37.5 Reorder the terms: -12.5 + x = -37.5 Solving -12.5 + x = -37.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -37.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -37.5 + 12.5 x = -37.5 + 12.5 Combine like terms: -37.5 + 12.5 = -25 x = -25 Simplifying x = -25Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -25}
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