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Simplifying 10x2 + -11x + 2.5 = 0 Reorder the terms: 2.5 + -11x + 10x2 = 0 Solving 2.5 + -11x + 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'. 0.25 + -1.1x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.1x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.1x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.1x + x2 = 0 + -0.25 -1.1x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.1x + x2 = -0.25 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = -0.25 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = -0.25 + 0.3025 Combine like terms: -0.25 + 0.3025 = 0.0525 0.3025 + -1.1x + x2 = 0.0525 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.0525 Calculate the square root of the right side: 0.229128785 Break this problem into two subproblems by setting (x + -0.55) equal to 0.229128785 and -0.229128785.Subproblem 1
x + -0.55 = 0.229128785 Simplifying x + -0.55 = 0.229128785 Reorder the terms: -0.55 + x = 0.229128785 Solving -0.55 + x = 0.229128785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 0.229128785 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.229128785 + 0.55 x = 0.229128785 + 0.55 Combine like terms: 0.229128785 + 0.55 = 0.779128785 x = 0.779128785 Simplifying x = 0.779128785Subproblem 2
x + -0.55 = -0.229128785 Simplifying x + -0.55 = -0.229128785 Reorder the terms: -0.55 + x = -0.229128785 Solving -0.55 + x = -0.229128785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -0.229128785 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.229128785 + 0.55 x = -0.229128785 + 0.55 Combine like terms: -0.229128785 + 0.55 = 0.320871215 x = 0.320871215 Simplifying x = 0.320871215Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.779128785, 0.320871215}
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