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Simplifying 4x2 + 31x + 21x = 110 Reorder the terms: 31x + 21x + 4x2 = 110 Combine like terms: 31x + 21x = 52x 52x + 4x2 = 110 Solving 52x + 4x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 52x + 4x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 52x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 26x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 26x + 2x2)' equal to zero and attempt to solve: Simplifying -55 + 26x + 2x2 = 0 Solving -55 + 26x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + 13x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 13x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 13x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 13x + x2 = 0 + 27.5 13x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 13x + x2 = 27.5 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 27.5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 27.5 + 42.25 Combine like terms: 27.5 + 42.25 = 69.75 42.25 + 13x + x2 = 69.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 69.75 Calculate the square root of the right side: 8.351646544 Break this problem into two subproblems by setting (x + 6.5) equal to 8.351646544 and -8.351646544.Subproblem 1
x + 6.5 = 8.351646544 Simplifying x + 6.5 = 8.351646544 Reorder the terms: 6.5 + x = 8.351646544 Solving 6.5 + x = 8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.351646544 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.351646544 + -6.5 x = 8.351646544 + -6.5 Combine like terms: 8.351646544 + -6.5 = 1.851646544 x = 1.851646544 Simplifying x = 1.851646544Subproblem 2
x + 6.5 = -8.351646544 Simplifying x + 6.5 = -8.351646544 Reorder the terms: 6.5 + x = -8.351646544 Solving 6.5 + x = -8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.351646544 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.351646544 + -6.5 x = -8.351646544 + -6.5 Combine like terms: -8.351646544 + -6.5 = -14.851646544 x = -14.851646544 Simplifying x = -14.851646544Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.851646544, -14.851646544}Solution
x = {1.851646544, -14.851646544}
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