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Simplifying -0.4x2 + 28x + -200 = 0 Reorder the terms: -200 + 28x + -0.4x2 = 0 Solving -200 + 28x + -0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 500 + -70x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -70x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -70x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -70x + x2 = 0 + -500 -70x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -70x + x2 = -500 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -500 + 1225 Reorder the terms: 1225 + -70x + x2 = -500 + 1225 Combine like terms: -500 + 1225 = 725 1225 + -70x + x2 = 725 Factor a perfect square on the left side: (x + -35)(x + -35) = 725 Calculate the square root of the right side: 26.925824036 Break this problem into two subproblems by setting (x + -35) equal to 26.925824036 and -26.925824036.Subproblem 1
x + -35 = 26.925824036 Simplifying x + -35 = 26.925824036 Reorder the terms: -35 + x = 26.925824036 Solving -35 + x = 26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 26.925824036 + 35 Combine like terms: -35 + 35 = 0 0 + x = 26.925824036 + 35 x = 26.925824036 + 35 Combine like terms: 26.925824036 + 35 = 61.925824036 x = 61.925824036 Simplifying x = 61.925824036Subproblem 2
x + -35 = -26.925824036 Simplifying x + -35 = -26.925824036 Reorder the terms: -35 + x = -26.925824036 Solving -35 + x = -26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -26.925824036 + 35 Combine like terms: -35 + 35 = 0 0 + x = -26.925824036 + 35 x = -26.925824036 + 35 Combine like terms: -26.925824036 + 35 = 8.074175964 x = 8.074175964 Simplifying x = 8.074175964Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.925824036, 8.074175964}
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