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Simplifying 33600 + -140x + -1x2 = 0 Solving 33600 + -140x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33600 + 140x + x2 = 0 Move the constant term to the right: Add '33600' to each side of the equation. -33600 + 140x + 33600 + x2 = 0 + 33600 Reorder the terms: -33600 + 33600 + 140x + x2 = 0 + 33600 Combine like terms: -33600 + 33600 = 0 0 + 140x + x2 = 0 + 33600 140x + x2 = 0 + 33600 Combine like terms: 0 + 33600 = 33600 140x + x2 = 33600 The x term is 140x. Take half its coefficient (70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. 140x + 4900 + x2 = 33600 + 4900 Reorder the terms: 4900 + 140x + x2 = 33600 + 4900 Combine like terms: 33600 + 4900 = 38500 4900 + 140x + x2 = 38500 Factor a perfect square on the left side: (x + 70)(x + 70) = 38500 Calculate the square root of the right side: 196.214168703 Break this problem into two subproblems by setting (x + 70) equal to 196.214168703 and -196.214168703.Subproblem 1
x + 70 = 196.214168703 Simplifying x + 70 = 196.214168703 Reorder the terms: 70 + x = 196.214168703 Solving 70 + x = 196.214168703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + x = 196.214168703 + -70 Combine like terms: 70 + -70 = 0 0 + x = 196.214168703 + -70 x = 196.214168703 + -70 Combine like terms: 196.214168703 + -70 = 126.214168703 x = 126.214168703 Simplifying x = 126.214168703Subproblem 2
x + 70 = -196.214168703 Simplifying x + 70 = -196.214168703 Reorder the terms: 70 + x = -196.214168703 Solving 70 + x = -196.214168703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + x = -196.214168703 + -70 Combine like terms: 70 + -70 = 0 0 + x = -196.214168703 + -70 x = -196.214168703 + -70 Combine like terms: -196.214168703 + -70 = -266.214168703 x = -266.214168703 Simplifying x = -266.214168703Solution
The solution to the problem is based on the solutions from the subproblems. x = {126.214168703, -266.214168703}
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