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Simplifying 10x2 + 10x + -2673 = 0 Reorder the terms: -2673 + 10x + 10x2 = 0 Solving -2673 + 10x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -267.3 + x + x2 = 0 Move the constant term to the right: Add '267.3' to each side of the equation. -267.3 + x + 267.3 + x2 = 0 + 267.3 Reorder the terms: -267.3 + 267.3 + x + x2 = 0 + 267.3 Combine like terms: -267.3 + 267.3 = 0.0 0.0 + x + x2 = 0 + 267.3 x + x2 = 0 + 267.3 Combine like terms: 0 + 267.3 = 267.3 x + x2 = 267.3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 267.3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 267.3 + 0.25 Combine like terms: 267.3 + 0.25 = 267.55 1.25 + x2 = 267.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 267.55 Calculate the square root of the right side: 16.356955707 Break this problem into two subproblems by setting (x + 0.5) equal to 16.356955707 and -16.356955707.Subproblem 1
x + 0.5 = 16.356955707 Simplifying x + 0.5 = 16.356955707 Reorder the terms: 0.5 + x = 16.356955707 Solving 0.5 + x = 16.356955707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 16.356955707 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.356955707 + -0.5 x = 16.356955707 + -0.5 Combine like terms: 16.356955707 + -0.5 = 15.856955707 x = 15.856955707 Simplifying x = 15.856955707Subproblem 2
x + 0.5 = -16.356955707 Simplifying x + 0.5 = -16.356955707 Reorder the terms: 0.5 + x = -16.356955707 Solving 0.5 + x = -16.356955707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -16.356955707 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.356955707 + -0.5 x = -16.356955707 + -0.5 Combine like terms: -16.356955707 + -0.5 = -16.856955707 x = -16.856955707 Simplifying x = -16.856955707Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.856955707, -16.856955707}
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