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Simplifying 62x + -1x2 = 35 Solving 62x + -1x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 62x + -1x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 62x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 35 + -62x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -62x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -62x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -62x + x2 = 0 + -35 -62x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -62x + x2 = -35 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 = -35 + 961 Reorder the terms: 961 + -62x + x2 = -35 + 961 Combine like terms: -35 + 961 = 926 961 + -62x + x2 = 926 Factor a perfect square on the left side: (x + -31)(x + -31) = 926 Calculate the square root of the right side: 30.430248109 Break this problem into two subproblems by setting (x + -31) equal to 30.430248109 and -30.430248109.Subproblem 1
x + -31 = 30.430248109 Simplifying x + -31 = 30.430248109 Reorder the terms: -31 + x = 30.430248109 Solving -31 + x = 30.430248109 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 = 30.430248109 + 31 Combine like terms: -31 + 31 = 0 0 + x = 30.430248109 + 31 x = 30.430248109 + 31 Combine like terms: 30.430248109 + 31 = 61.430248109 x = 61.430248109 Simplifying x = 61.430248109Subproblem 2
x + -31 = -30.430248109 Simplifying x + -31 = -30.430248109 Reorder the terms: -31 + x = -30.430248109 Solving -31 + x = -30.430248109 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 = -30.430248109 + 31 Combine like terms: -31 + 31 = 0 0 + x = -30.430248109 + 31 x = -30.430248109 + 31 Combine like terms: -30.430248109 + 31 = 0.569751891 x = 0.569751891 Simplifying x = 0.569751891Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.430248109, 0.569751891}
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