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Simplifying 0 = x2 + 35x + -24 Reorder the terms: 0 = -24 + 35x + x2 Solving 0 = -24 + 35x + x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -35x + -1x2 = -24 + 35x + x2 + 24 + -35x + -1x2 Reorder the terms: 24 + -35x + -1x2 = -24 + 24 + 35x + -35x + x2 + -1x2 Combine like terms: -24 + 24 = 0 24 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2 24 + -35x + -1x2 = 35x + -35x + x2 + -1x2 Combine like terms: 35x + -35x = 0 24 + -35x + -1x2 = 0 + x2 + -1x2 24 + -35x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + -35x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 35x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 35x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 35x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 35x + x2 = 0 + 24 35x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 35x + x2 = 24 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 24 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 24 + 306.25 Combine like terms: 24 + 306.25 = 330.25 306.25 + 35x + x2 = 330.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 330.25 Calculate the square root of the right side: 18.172781845 Break this problem into two subproblems by setting (x + 17.5) equal to 18.172781845 and -18.172781845.Subproblem 1
x + 17.5 = 18.172781845 Simplifying x + 17.5 = 18.172781845 Reorder the terms: 17.5 + x = 18.172781845 Solving 17.5 + x = 18.172781845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 18.172781845 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 18.172781845 + -17.5 x = 18.172781845 + -17.5 Combine like terms: 18.172781845 + -17.5 = 0.672781845 x = 0.672781845 Simplifying x = 0.672781845Subproblem 2
x + 17.5 = -18.172781845 Simplifying x + 17.5 = -18.172781845 Reorder the terms: 17.5 + x = -18.172781845 Solving 17.5 + x = -18.172781845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -18.172781845 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -18.172781845 + -17.5 x = -18.172781845 + -17.5 Combine like terms: -18.172781845 + -17.5 = -35.672781845 x = -35.672781845 Simplifying x = -35.672781845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.672781845, -35.672781845}
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