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Simplifying 40x2 + -44x + 11 = 0 Reorder the terms: 11 + -44x + 40x2 = 0 Solving 11 + -44x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.275 + -1.1x + x2 = 0 Move the constant term to the right: Add '-0.275' to each side of the equation. 0.275 + -1.1x + -0.275 + x2 = 0 + -0.275 Reorder the terms: 0.275 + -0.275 + -1.1x + x2 = 0 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + -1.1x + x2 = 0 + -0.275 -1.1x + x2 = 0 + -0.275 Combine like terms: 0 + -0.275 = -0.275 -1.1x + x2 = -0.275 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 = -0.275 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = -0.275 + 0.3025 Combine like terms: -0.275 + 0.3025 = 0.0275 0.3025 + -1.1x + x2 = 0.0275 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.0275 Calculate the square root of the right side: 0.16583124 Break this problem into two subproblems by setting (x + -0.55) equal to 0.16583124 and -0.16583124.Subproblem 1
x + -0.55 = 0.16583124 Simplifying x + -0.55 = 0.16583124 Reorder the terms: -0.55 + x = 0.16583124 Solving -0.55 + x = 0.16583124 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 = 0.16583124 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.16583124 + 0.55 x = 0.16583124 + 0.55 Combine like terms: 0.16583124 + 0.55 = 0.71583124 x = 0.71583124 Simplifying x = 0.71583124Subproblem 2
x + -0.55 = -0.16583124 Simplifying x + -0.55 = -0.16583124 Reorder the terms: -0.55 + x = -0.16583124 Solving -0.55 + x = -0.16583124 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 = -0.16583124 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.16583124 + 0.55 x = -0.16583124 + 0.55 Combine like terms: -0.16583124 + 0.55 = 0.38416876 x = 0.38416876 Simplifying x = 0.38416876Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71583124, 0.38416876}
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