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Simplifying 8 = -0.004x2 + 0.3x + 6 Reorder the terms: 8 = 6 + 0.3x + -0.004x2 Solving 8 = 6 + 0.3x + -0.004x2 Solving for variable 'x'. Combine like terms: 8 + -6 = 2 2 + -0.3x + 0.004x2 = 6 + 0.3x + -0.004x2 + -6 + -0.3x + 0.004x2 Reorder the terms: 2 + -0.3x + 0.004x2 = 6 + -6 + 0.3x + -0.3x + -0.004x2 + 0.004x2 Combine like terms: 6 + -6 = 0 2 + -0.3x + 0.004x2 = 0 + 0.3x + -0.3x + -0.004x2 + 0.004x2 2 + -0.3x + 0.004x2 = 0.3x + -0.3x + -0.004x2 + 0.004x2 Combine like terms: 0.3x + -0.3x = 0.0 2 + -0.3x + 0.004x2 = 0.0 + -0.004x2 + 0.004x2 2 + -0.3x + 0.004x2 = -0.004x2 + 0.004x2 Combine like terms: -0.004x2 + 0.004x2 = 0.000 2 + -0.3x + 0.004x2 = 0.000 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. 500 + -75x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -75x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -75x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -75x + x2 = 0 + -500 -75x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -75x + x2 = -500 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -500 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -500 + 1406.25 Combine like terms: -500 + 1406.25 = 906.25 1406.25 + -75x + x2 = 906.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 906.25 Calculate the square root of the right side: 30.103986447 Break this problem into two subproblems by setting (x + -37.5) equal to 30.103986447 and -30.103986447.Subproblem 1
x + -37.5 = 30.103986447 Simplifying x + -37.5 = 30.103986447 Reorder the terms: -37.5 + x = 30.103986447 Solving -37.5 + x = 30.103986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 30.103986447 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 30.103986447 + 37.5 x = 30.103986447 + 37.5 Combine like terms: 30.103986447 + 37.5 = 67.603986447 x = 67.603986447 Simplifying x = 67.603986447Subproblem 2
x + -37.5 = -30.103986447 Simplifying x + -37.5 = -30.103986447 Reorder the terms: -37.5 + x = -30.103986447 Solving -37.5 + x = -30.103986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -30.103986447 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -30.103986447 + 37.5 x = -30.103986447 + 37.5 Combine like terms: -30.103986447 + 37.5 = 7.396013553 x = 7.396013553 Simplifying x = 7.396013553Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.603986447, 7.396013553}
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