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Simplifying -25x2 = 35x + 1 Reorder the terms: -25x2 = 1 + 35x Solving -25x2 = 1 + 35x Solving for variable 'x'. Reorder the terms: -1 + -35x + -25x2 = 1 + 35x + -1 + -35x Reorder the terms: -1 + -35x + -25x2 = 1 + -1 + 35x + -35x Combine like terms: 1 + -1 = 0 -1 + -35x + -25x2 = 0 + 35x + -35x -1 + -35x + -25x2 = 35x + -35x Combine like terms: 35x + -35x = 0 -1 + -35x + -25x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 35x + 25x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 35x + 25x2)' equal to zero and attempt to solve: Simplifying 1 + 35x + 25x2 = 0 Solving 1 + 35x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.04 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 1.4x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 1.4x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 1.4x + x2 = 0 + -0.04 1.4x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 1.4x + x2 = -0.04 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.04 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.04 + 0.49 Combine like terms: -0.04 + 0.49 = 0.45 0.49 + 1.4x + x2 = 0.45 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + 0.7) equal to 0.670820393 and -0.670820393.Subproblem 1
x + 0.7 = 0.670820393 Simplifying x + 0.7 = 0.670820393 Reorder the terms: 0.7 + x = 0.670820393 Solving 0.7 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.670820393 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.670820393 + -0.7 x = 0.670820393 + -0.7 Combine like terms: 0.670820393 + -0.7 = -0.029179607 x = -0.029179607 Simplifying x = -0.029179607Subproblem 2
x + 0.7 = -0.670820393 Simplifying x + 0.7 = -0.670820393 Reorder the terms: 0.7 + x = -0.670820393 Solving 0.7 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.670820393 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.670820393 + -0.7 x = -0.670820393 + -0.7 Combine like terms: -0.670820393 + -0.7 = -1.370820393 x = -1.370820393 Simplifying x = -1.370820393Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.029179607, -1.370820393}Solution
x = {-0.029179607, -1.370820393}
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