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Simplifying 2x2 + -10 = -38x + -98 Reorder the terms: -10 + 2x2 = -38x + -98 Reorder the terms: -10 + 2x2 = -98 + -38x Solving -10 + 2x2 = -98 + -38x Solving for variable 'x'. Reorder the terms: -10 + 98 + 38x + 2x2 = -98 + -38x + 98 + 38x Combine like terms: -10 + 98 = 88 88 + 38x + 2x2 = -98 + -38x + 98 + 38x Reorder the terms: 88 + 38x + 2x2 = -98 + 98 + -38x + 38x Combine like terms: -98 + 98 = 0 88 + 38x + 2x2 = 0 + -38x + 38x 88 + 38x + 2x2 = -38x + 38x Combine like terms: -38x + 38x = 0 88 + 38x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(44 + 19x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(44 + 19x + x2)' equal to zero and attempt to solve: Simplifying 44 + 19x + x2 = 0 Solving 44 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 19x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + 19x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 19x + x2 = 0 + -44 19x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 19x + x2 = -44 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 = -44 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -44 + 90.25 Combine like terms: -44 + 90.25 = 46.25 90.25 + 19x + x2 = 46.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + 9.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + 9.5 = 6.800735254 Simplifying x + 9.5 = 6.800735254 Reorder the terms: 9.5 + x = 6.800735254 Solving 9.5 + x = 6.800735254 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 = 6.800735254 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 6.800735254 + -9.5 x = 6.800735254 + -9.5 Combine like terms: 6.800735254 + -9.5 = -2.699264746 x = -2.699264746 Simplifying x = -2.699264746Subproblem 2
x + 9.5 = -6.800735254 Simplifying x + 9.5 = -6.800735254 Reorder the terms: 9.5 + x = -6.800735254 Solving 9.5 + x = -6.800735254 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 = -6.800735254 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -6.800735254 + -9.5 x = -6.800735254 + -9.5 Combine like terms: -6.800735254 + -9.5 = -16.300735254 x = -16.300735254 Simplifying x = -16.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.699264746, -16.300735254}Solution
x = {-2.699264746, -16.300735254}
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