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Simplifying -0.5x2 + 35x + -150 = 0 Reorder the terms: -150 + 35x + -0.5x2 = 0 Solving -150 + 35x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 300 + -70x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -70x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -70x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -70x + x2 = 0 + -300 -70x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -70x + x2 = -300 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 = -300 + 1225 Reorder the terms: 1225 + -70x + x2 = -300 + 1225 Combine like terms: -300 + 1225 = 925 1225 + -70x + x2 = 925 Factor a perfect square on the left side: (x + -35)(x + -35) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (x + -35) equal to 30.413812651 and -30.413812651.Subproblem 1
x + -35 = 30.413812651 Simplifying x + -35 = 30.413812651 Reorder the terms: -35 + x = 30.413812651 Solving -35 + x = 30.413812651 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 = 30.413812651 + 35 Combine like terms: -35 + 35 = 0 0 + x = 30.413812651 + 35 x = 30.413812651 + 35 Combine like terms: 30.413812651 + 35 = 65.413812651 x = 65.413812651 Simplifying x = 65.413812651Subproblem 2
x + -35 = -30.413812651 Simplifying x + -35 = -30.413812651 Reorder the terms: -35 + x = -30.413812651 Solving -35 + x = -30.413812651 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 = -30.413812651 + 35 Combine like terms: -35 + 35 = 0 0 + x = -30.413812651 + 35 x = -30.413812651 + 35 Combine like terms: -30.413812651 + 35 = 4.586187349 x = 4.586187349 Simplifying x = 4.586187349Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.413812651, 4.586187349}
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