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Simplifying 2x2 + 26x + 45 = 0 Reorder the terms: 45 + 26x + 2x2 = 0 Solving 45 + 26x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 13x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 13x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 13x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 13x + x2 = 0 + -22.5 13x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 13x + x2 = -22.5 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 = -22.5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -22.5 + 42.25 Combine like terms: -22.5 + 42.25 = 19.75 42.25 + 13x + x2 = 19.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + 6.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + 6.5 = 4.444097209 Simplifying x + 6.5 = 4.444097209 Reorder the terms: 6.5 + x = 4.444097209 Solving 6.5 + x = 4.444097209 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 = 4.444097209 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 4.444097209 + -6.5 x = 4.444097209 + -6.5 Combine like terms: 4.444097209 + -6.5 = -2.055902791 x = -2.055902791 Simplifying x = -2.055902791Subproblem 2
x + 6.5 = -4.444097209 Simplifying x + 6.5 = -4.444097209 Reorder the terms: 6.5 + x = -4.444097209 Solving 6.5 + x = -4.444097209 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 = -4.444097209 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -4.444097209 + -6.5 x = -4.444097209 + -6.5 Combine like terms: -4.444097209 + -6.5 = -10.944097209 x = -10.944097209 Simplifying x = -10.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.055902791, -10.944097209}
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