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Simplifying 5x + 25 + -50x = -4x2 + -20 Reorder the terms: 25 + 5x + -50x = -4x2 + -20 Combine like terms: 5x + -50x = -45x 25 + -45x = -4x2 + -20 Reorder the terms: 25 + -45x = -20 + -4x2 Solving 25 + -45x = -20 + -4x2 Solving for variable 'x'. Reorder the terms: 25 + 20 + -45x + 4x2 = -20 + -4x2 + 20 + 4x2 Combine like terms: 25 + 20 = 45 45 + -45x + 4x2 = -20 + -4x2 + 20 + 4x2 Reorder the terms: 45 + -45x + 4x2 = -20 + 20 + -4x2 + 4x2 Combine like terms: -20 + 20 = 0 45 + -45x + 4x2 = 0 + -4x2 + 4x2 45 + -45x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 45 + -45x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + -11.25x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + -11.25x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + -11.25x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + -11.25x + x2 = 0 + -11.25 -11.25x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 -11.25x + x2 = -11.25 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -11.25 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -11.25 + 31.640625 Combine like terms: -11.25 + 31.640625 = 20.390625 31.640625 + -11.25x + x2 = 20.390625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 20.390625 Calculate the square root of the right side: 4.515597967 Break this problem into two subproblems by setting (x + -5.625) equal to 4.515597967 and -4.515597967.Subproblem 1
x + -5.625 = 4.515597967 Simplifying x + -5.625 = 4.515597967 Reorder the terms: -5.625 + x = 4.515597967 Solving -5.625 + x = 4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 4.515597967 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 4.515597967 + 5.625 x = 4.515597967 + 5.625 Combine like terms: 4.515597967 + 5.625 = 10.140597967 x = 10.140597967 Simplifying x = 10.140597967Subproblem 2
x + -5.625 = -4.515597967 Simplifying x + -5.625 = -4.515597967 Reorder the terms: -5.625 + x = -4.515597967 Solving -5.625 + x = -4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -4.515597967 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -4.515597967 + 5.625 x = -4.515597967 + 5.625 Combine like terms: -4.515597967 + 5.625 = 1.109402033 x = 1.109402033 Simplifying x = 1.109402033Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.140597967, 1.109402033}
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