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Simplifying 0 = -10x + 25 + x2 + -20x + 10 Reorder the terms: 0 = 25 + 10 + -10x + -20x + x2 Combine like terms: 25 + 10 = 35 0 = 35 + -10x + -20x + x2 Combine like terms: -10x + -20x = -30x 0 = 35 + -30x + x2 Solving 0 = 35 + -30x + x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + 30x + -1x2 = 35 + -30x + x2 + -35 + 30x + -1x2 Reorder the terms: -35 + 30x + -1x2 = 35 + -35 + -30x + 30x + x2 + -1x2 Combine like terms: 35 + -35 = 0 -35 + 30x + -1x2 = 0 + -30x + 30x + x2 + -1x2 -35 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 -35 + 30x + -1x2 = 0 + x2 + -1x2 -35 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -35 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 35 + -30x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -30x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -30x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -30x + x2 = 0 + -35 -30x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -30x + x2 = -35 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -35 + 225 Reorder the terms: 225 + -30x + x2 = -35 + 225 Combine like terms: -35 + 225 = 190 225 + -30x + x2 = 190 Factor a perfect square on the left side: (x + -15)(x + -15) = 190 Calculate the square root of the right side: 13.784048752 Break this problem into two subproblems by setting (x + -15) equal to 13.784048752 and -13.784048752.Subproblem 1
x + -15 = 13.784048752 Simplifying x + -15 = 13.784048752 Reorder the terms: -15 + x = 13.784048752 Solving -15 + x = 13.784048752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.784048752 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.784048752 + 15 x = 13.784048752 + 15 Combine like terms: 13.784048752 + 15 = 28.784048752 x = 28.784048752 Simplifying x = 28.784048752Subproblem 2
x + -15 = -13.784048752 Simplifying x + -15 = -13.784048752 Reorder the terms: -15 + x = -13.784048752 Solving -15 + x = -13.784048752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.784048752 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.784048752 + 15 x = -13.784048752 + 15 Combine like terms: -13.784048752 + 15 = 1.215951248 x = 1.215951248 Simplifying x = 1.215951248Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.784048752, 1.215951248}
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