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Simplifying 0.5x2 + 35x + -20 = 0 Reorder the terms: -20 + 35x + 0.5x2 = 0 Solving -20 + 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'. -40 + 70x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 70x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 70x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 70x + x2 = 0 + 40 70x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 70x + x2 = 40 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 = 40 + 1225 Reorder the terms: 1225 + 70x + x2 = 40 + 1225 Combine like terms: 40 + 1225 = 1265 1225 + 70x + x2 = 1265 Factor a perfect square on the left side: (x + 35)(x + 35) = 1265 Calculate the square root of the right side: 35.566838488 Break this problem into two subproblems by setting (x + 35) equal to 35.566838488 and -35.566838488.Subproblem 1
x + 35 = 35.566838488 Simplifying x + 35 = 35.566838488 Reorder the terms: 35 + x = 35.566838488 Solving 35 + x = 35.566838488 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 = 35.566838488 + -35 Combine like terms: 35 + -35 = 0 0 + x = 35.566838488 + -35 x = 35.566838488 + -35 Combine like terms: 35.566838488 + -35 = 0.566838488 x = 0.566838488 Simplifying x = 0.566838488Subproblem 2
x + 35 = -35.566838488 Simplifying x + 35 = -35.566838488 Reorder the terms: 35 + x = -35.566838488 Solving 35 + x = -35.566838488 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 = -35.566838488 + -35 Combine like terms: 35 + -35 = 0 0 + x = -35.566838488 + -35 x = -35.566838488 + -35 Combine like terms: -35.566838488 + -35 = -70.566838488 x = -70.566838488 Simplifying x = -70.566838488Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.566838488, -70.566838488}
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