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Simplifying 0 = -1x + 20x + 97 + -1x2 Reorder the terms: 0 = 97 + -1x + 20x + -1x2 Combine like terms: -1x + 20x = 19x 0 = 97 + 19x + -1x2 Solving 0 = 97 + 19x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -97 = -97 -97 + -19x + x2 = 97 + 19x + -1x2 + -97 + -19x + x2 Reorder the terms: -97 + -19x + x2 = 97 + -97 + 19x + -19x + -1x2 + x2 Combine like terms: 97 + -97 = 0 -97 + -19x + x2 = 0 + 19x + -19x + -1x2 + x2 -97 + -19x + x2 = 19x + -19x + -1x2 + x2 Combine like terms: 19x + -19x = 0 -97 + -19x + x2 = 0 + -1x2 + x2 -97 + -19x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -97 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -19x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + -19x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -19x + x2 = 0 + 97 -19x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 -19x + x2 = 97 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 97 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 97 + 90.25 Combine like terms: 97 + 90.25 = 187.25 90.25 + -19x + x2 = 187.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 187.25 Calculate the square root of the right side: 13.683932183 Break this problem into two subproblems by setting (x + -9.5) equal to 13.683932183 and -13.683932183.Subproblem 1
x + -9.5 = 13.683932183 Simplifying x + -9.5 = 13.683932183 Reorder the terms: -9.5 + x = 13.683932183 Solving -9.5 + x = 13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 13.683932183 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 13.683932183 + 9.5 x = 13.683932183 + 9.5 Combine like terms: 13.683932183 + 9.5 = 23.183932183 x = 23.183932183 Simplifying x = 23.183932183Subproblem 2
x + -9.5 = -13.683932183 Simplifying x + -9.5 = -13.683932183 Reorder the terms: -9.5 + x = -13.683932183 Solving -9.5 + x = -13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -13.683932183 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -13.683932183 + 9.5 x = -13.683932183 + 9.5 Combine like terms: -13.683932183 + 9.5 = -4.183932183 x = -4.183932183 Simplifying x = -4.183932183Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.183932183, -4.183932183}
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