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Simplifying 40 + -26x + 4x2 = 30 Solving 40 + -26x + 4x2 = 30 Solving for variable 'x'. Reorder the terms: 40 + -30 + -26x + 4x2 = 30 + -30 Combine like terms: 40 + -30 = 10 10 + -26x + 4x2 = 30 + -30 Combine like terms: 30 + -30 = 0 10 + -26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -13x + 2x2 = 0 Solving 5 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -6.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -6.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -6.5x + x2 = 0 + -2.5 -6.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -6.5x + x2 = -2.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -2.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -2.5 + 10.5625 Combine like terms: -2.5 + 10.5625 = 8.0625 10.5625 + -6.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -3.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -3.25 = 2.839454173 Simplifying x + -3.25 = 2.839454173 Reorder the terms: -3.25 + x = 2.839454173 Solving -3.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.839454173 + 3.25 x = 2.839454173 + 3.25 Combine like terms: 2.839454173 + 3.25 = 6.089454173 x = 6.089454173 Simplifying x = 6.089454173Subproblem 2
x + -3.25 = -2.839454173 Simplifying x + -3.25 = -2.839454173 Reorder the terms: -3.25 + x = -2.839454173 Solving -3.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.839454173 + 3.25 x = -2.839454173 + 3.25 Combine like terms: -2.839454173 + 3.25 = 0.410545827 x = 0.410545827 Simplifying x = 0.410545827Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.089454173, 0.410545827}Solution
x = {6.089454173, 0.410545827}
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