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Simplifying x2 + -19x + 10 = 20 Reorder the terms: 10 + -19x + x2 = 20 Solving 10 + -19x + x2 = 20 Solving for variable 'x'. Reorder the terms: 10 + -20 + -19x + x2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + -19x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -19x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -19x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -19x + x2 = 0 + 10 -19x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -19x + x2 = 10 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 = 10 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 10 + 90.25 Combine like terms: 10 + 90.25 = 100.25 90.25 + -19x + x2 = 100.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -9.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -9.5 = 10.012492197 Simplifying x + -9.5 = 10.012492197 Reorder the terms: -9.5 + x = 10.012492197 Solving -9.5 + x = 10.012492197 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 = 10.012492197 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.012492197 + 9.5 x = 10.012492197 + 9.5 Combine like terms: 10.012492197 + 9.5 = 19.512492197 x = 19.512492197 Simplifying x = 19.512492197Subproblem 2
x + -9.5 = -10.012492197 Simplifying x + -9.5 = -10.012492197 Reorder the terms: -9.5 + x = -10.012492197 Solving -9.5 + x = -10.012492197 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 = -10.012492197 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.012492197 + 9.5 x = -10.012492197 + 9.5 Combine like terms: -10.012492197 + 9.5 = -0.512492197 x = -0.512492197 Simplifying x = -0.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.512492197, -0.512492197}
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