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Simplifying x2 + -35x + 76 = 0 Reorder the terms: 76 + -35x + x2 = 0 Solving 76 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + -35x + -76 + x2 = 0 + -76 Reorder the terms: 76 + -76 + -35x + x2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + -35x + x2 = 0 + -76 -35x + x2 = 0 + -76 Combine like terms: 0 + -76 = -76 -35x + x2 = -76 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 = -76 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -76 + 306.25 Combine like terms: -76 + 306.25 = 230.25 306.25 + -35x + x2 = 230.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (x + -17.5) equal to 15.173990905 and -15.173990905.Subproblem 1
x + -17.5 = 15.173990905 Simplifying x + -17.5 = 15.173990905 Reorder the terms: -17.5 + x = 15.173990905 Solving -17.5 + x = 15.173990905 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 = 15.173990905 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 15.173990905 + 17.5 x = 15.173990905 + 17.5 Combine like terms: 15.173990905 + 17.5 = 32.673990905 x = 32.673990905 Simplifying x = 32.673990905Subproblem 2
x + -17.5 = -15.173990905 Simplifying x + -17.5 = -15.173990905 Reorder the terms: -17.5 + x = -15.173990905 Solving -17.5 + x = -15.173990905 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 = -15.173990905 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -15.173990905 + 17.5 x = -15.173990905 + 17.5 Combine like terms: -15.173990905 + 17.5 = 2.326009095 x = 2.326009095 Simplifying x = 2.326009095Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.673990905, 2.326009095}
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