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Simplifying 0 = x2 + -62x + 44 Reorder the terms: 0 = 44 + -62x + x2 Solving 0 = 44 + -62x + x2 Solving for variable 'x'. Combine like terms: 0 + -44 = -44 -44 + 62x + -1x2 = 44 + -62x + x2 + -44 + 62x + -1x2 Reorder the terms: -44 + 62x + -1x2 = 44 + -44 + -62x + 62x + x2 + -1x2 Combine like terms: 44 + -44 = 0 -44 + 62x + -1x2 = 0 + -62x + 62x + x2 + -1x2 -44 + 62x + -1x2 = -62x + 62x + x2 + -1x2 Combine like terms: -62x + 62x = 0 -44 + 62x + -1x2 = 0 + x2 + -1x2 -44 + 62x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -44 + 62x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 44 + -62x + x2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -62x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + -62x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -62x + x2 = 0 + -44 -62x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 -62x + x2 = -44 The x term is -62x. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62x + 961 + x2 = -44 + 961 Reorder the terms: 961 + -62x + x2 = -44 + 961 Combine like terms: -44 + 961 = 917 961 + -62x + x2 = 917 Factor a perfect square on the left side: (x + -31)(x + -31) = 917 Calculate the square root of the right side: 30.282007859 Break this problem into two subproblems by setting (x + -31) equal to 30.282007859 and -30.282007859.Subproblem 1
x + -31 = 30.282007859 Simplifying x + -31 = 30.282007859 Reorder the terms: -31 + x = 30.282007859 Solving -31 + x = 30.282007859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 30.282007859 + 31 Combine like terms: -31 + 31 = 0 0 + x = 30.282007859 + 31 x = 30.282007859 + 31 Combine like terms: 30.282007859 + 31 = 61.282007859 x = 61.282007859 Simplifying x = 61.282007859Subproblem 2
x + -31 = -30.282007859 Simplifying x + -31 = -30.282007859 Reorder the terms: -31 + x = -30.282007859 Solving -31 + x = -30.282007859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = -30.282007859 + 31 Combine like terms: -31 + 31 = 0 0 + x = -30.282007859 + 31 x = -30.282007859 + 31 Combine like terms: -30.282007859 + 31 = 0.717992141 x = 0.717992141 Simplifying x = 0.717992141Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.282007859, 0.717992141}
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