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Simplifying 5.32x2 + -11.42x + 2.74 = 0 Reorder the terms: 2.74 + -11.42x + 5.32x2 = 0 Solving 2.74 + -11.42x + 5.32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.32 the coefficient of the squared term: Divide each side by '5.32'. 0.515037594 + -2.146616541x + x2 = 0 Move the constant term to the right: Add '-0.515037594' to each side of the equation. 0.515037594 + -2.146616541x + -0.515037594 + x2 = 0 + -0.515037594 Reorder the terms: 0.515037594 + -0.515037594 + -2.146616541x + x2 = 0 + -0.515037594 Combine like terms: 0.515037594 + -0.515037594 = 0.000000000 0.000000000 + -2.146616541x + x2 = 0 + -0.515037594 -2.146616541x + x2 = 0 + -0.515037594 Combine like terms: 0 + -0.515037594 = -0.515037594 -2.146616541x + x2 = -0.515037594 The x term is -2.146616541x. Take half its coefficient (-1.073308271). Square it (1.151990645) and add it to both sides. Add '1.151990645' to each side of the equation. -2.146616541x + 1.151990645 + x2 = -0.515037594 + 1.151990645 Reorder the terms: 1.151990645 + -2.146616541x + x2 = -0.515037594 + 1.151990645 Combine like terms: -0.515037594 + 1.151990645 = 0.636953051 1.151990645 + -2.146616541x + x2 = 0.636953051 Factor a perfect square on the left side: (x + -1.073308271)(x + -1.073308271) = 0.636953051 Calculate the square root of the right side: 0.798093385 Break this problem into two subproblems by setting (x + -1.073308271) equal to 0.798093385 and -0.798093385.Subproblem 1
x + -1.073308271 = 0.798093385 Simplifying x + -1.073308271 = 0.798093385 Reorder the terms: -1.073308271 + x = 0.798093385 Solving -1.073308271 + x = 0.798093385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.073308271' to each side of the equation. -1.073308271 + 1.073308271 + x = 0.798093385 + 1.073308271 Combine like terms: -1.073308271 + 1.073308271 = 0.000000000 0.000000000 + x = 0.798093385 + 1.073308271 x = 0.798093385 + 1.073308271 Combine like terms: 0.798093385 + 1.073308271 = 1.871401656 x = 1.871401656 Simplifying x = 1.871401656Subproblem 2
x + -1.073308271 = -0.798093385 Simplifying x + -1.073308271 = -0.798093385 Reorder the terms: -1.073308271 + x = -0.798093385 Solving -1.073308271 + x = -0.798093385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.073308271' to each side of the equation. -1.073308271 + 1.073308271 + x = -0.798093385 + 1.073308271 Combine like terms: -1.073308271 + 1.073308271 = 0.000000000 0.000000000 + x = -0.798093385 + 1.073308271 x = -0.798093385 + 1.073308271 Combine like terms: -0.798093385 + 1.073308271 = 0.275214886 x = 0.275214886 Simplifying x = 0.275214886Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.871401656, 0.275214886}
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