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Simplifying x2 + -80x + -690 = 0 Reorder the terms: -690 + -80x + x2 = 0 Solving -690 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '690' to each side of the equation. -690 + -80x + 690 + x2 = 0 + 690 Reorder the terms: -690 + 690 + -80x + x2 = 0 + 690 Combine like terms: -690 + 690 = 0 0 + -80x + x2 = 0 + 690 -80x + x2 = 0 + 690 Combine like terms: 0 + 690 = 690 -80x + x2 = 690 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 690 + 1600 Reorder the terms: 1600 + -80x + x2 = 690 + 1600 Combine like terms: 690 + 1600 = 2290 1600 + -80x + x2 = 2290 Factor a perfect square on the left side: (x + -40)(x + -40) = 2290 Calculate the square root of the right side: 47.853944456 Break this problem into two subproblems by setting (x + -40) equal to 47.853944456 and -47.853944456.Subproblem 1
x + -40 = 47.853944456 Simplifying x + -40 = 47.853944456 Reorder the terms: -40 + x = 47.853944456 Solving -40 + x = 47.853944456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 47.853944456 + 40 Combine like terms: -40 + 40 = 0 0 + x = 47.853944456 + 40 x = 47.853944456 + 40 Combine like terms: 47.853944456 + 40 = 87.853944456 x = 87.853944456 Simplifying x = 87.853944456Subproblem 2
x + -40 = -47.853944456 Simplifying x + -40 = -47.853944456 Reorder the terms: -40 + x = -47.853944456 Solving -40 + x = -47.853944456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -47.853944456 + 40 Combine like terms: -40 + 40 = 0 0 + x = -47.853944456 + 40 x = -47.853944456 + 40 Combine like terms: -47.853944456 + 40 = -7.853944456 x = -7.853944456 Simplifying x = -7.853944456Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.853944456, -7.853944456}
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