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Simplifying -0.21x2 + 16x + 50 = 0 Reorder the terms: 50 + 16x + -0.21x2 = 0 Solving 50 + 16x + -0.21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.21 the coefficient of the squared term: Divide each side by '-0.21'. -238.0952381 + -76.19047619x + x2 = 0 Move the constant term to the right: Add '238.0952381' to each side of the equation. -238.0952381 + -76.19047619x + 238.0952381 + x2 = 0 + 238.0952381 Reorder the terms: -238.0952381 + 238.0952381 + -76.19047619x + x2 = 0 + 238.0952381 Combine like terms: -238.0952381 + 238.0952381 = 0.0000000 0.0000000 + -76.19047619x + x2 = 0 + 238.0952381 -76.19047619x + x2 = 0 + 238.0952381 Combine like terms: 0 + 238.0952381 = 238.0952381 -76.19047619x + x2 = 238.0952381 The x term is -76.19047619x. Take half its coefficient (-38.0952381). Square it (1451.247166) and add it to both sides. Add '1451.247166' to each side of the equation. -76.19047619x + 1451.247166 + x2 = 238.0952381 + 1451.247166 Reorder the terms: 1451.247166 + -76.19047619x + x2 = 238.0952381 + 1451.247166 Combine like terms: 238.0952381 + 1451.247166 = 1689.3424041 1451.247166 + -76.19047619x + x2 = 1689.3424041 Factor a perfect square on the left side: (x + -38.0952381)(x + -38.0952381) = 1689.3424041 Calculate the square root of the right side: 41.101610724 Break this problem into two subproblems by setting (x + -38.0952381) equal to 41.101610724 and -41.101610724.Subproblem 1
x + -38.0952381 = 41.101610724 Simplifying x + -38.0952381 = 41.101610724 Reorder the terms: -38.0952381 + x = 41.101610724 Solving -38.0952381 + x = 41.101610724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.0952381' to each side of the equation. -38.0952381 + 38.0952381 + x = 41.101610724 + 38.0952381 Combine like terms: -38.0952381 + 38.0952381 = 0.0000000 0.0000000 + x = 41.101610724 + 38.0952381 x = 41.101610724 + 38.0952381 Combine like terms: 41.101610724 + 38.0952381 = 79.196848824 x = 79.196848824 Simplifying x = 79.196848824Subproblem 2
x + -38.0952381 = -41.101610724 Simplifying x + -38.0952381 = -41.101610724 Reorder the terms: -38.0952381 + x = -41.101610724 Solving -38.0952381 + x = -41.101610724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.0952381' to each side of the equation. -38.0952381 + 38.0952381 + x = -41.101610724 + 38.0952381 Combine like terms: -38.0952381 + 38.0952381 = 0.0000000 0.0000000 + x = -41.101610724 + 38.0952381 x = -41.101610724 + 38.0952381 Combine like terms: -41.101610724 + 38.0952381 = -3.006372624 x = -3.006372624 Simplifying x = -3.006372624Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.196848824, -3.006372624}
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