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Simplifying 4x2 = 25x + 26 Reorder the terms: 4x2 = 26 + 25x Solving 4x2 = 26 + 25x Solving for variable 'x'. Reorder the terms: -26 + -25x + 4x2 = 26 + 25x + -26 + -25x Reorder the terms: -26 + -25x + 4x2 = 26 + -26 + 25x + -25x Combine like terms: 26 + -26 = 0 -26 + -25x + 4x2 = 0 + 25x + -25x -26 + -25x + 4x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -26 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -6.25x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -6.25x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -6.25x + x2 = 0 + 6.5 -6.25x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -6.25x + x2 = 6.5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 6.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 6.5 + 9.765625 Combine like terms: 6.5 + 9.765625 = 16.265625 9.765625 + -6.25x + x2 = 16.265625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 16.265625 Calculate the square root of the right side: 4.033066451 Break this problem into two subproblems by setting (x + -3.125) equal to 4.033066451 and -4.033066451.Subproblem 1
x + -3.125 = 4.033066451 Simplifying x + -3.125 = 4.033066451 Reorder the terms: -3.125 + x = 4.033066451 Solving -3.125 + x = 4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 4.033066451 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 4.033066451 + 3.125 x = 4.033066451 + 3.125 Combine like terms: 4.033066451 + 3.125 = 7.158066451 x = 7.158066451 Simplifying x = 7.158066451Subproblem 2
x + -3.125 = -4.033066451 Simplifying x + -3.125 = -4.033066451 Reorder the terms: -3.125 + x = -4.033066451 Solving -3.125 + x = -4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -4.033066451 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -4.033066451 + 3.125 x = -4.033066451 + 3.125 Combine like terms: -4.033066451 + 3.125 = -0.908066451 x = -0.908066451 Simplifying x = -0.908066451Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.158066451, -0.908066451}
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