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Simplifying 2x + -9 = -8x(5 + 5x) Reorder the terms: -9 + 2x = -8x(5 + 5x) -9 + 2x = (5 * -8x + 5x * -8x) -9 + 2x = (-40x + -40x2) Solving -9 + 2x = -40x + -40x2 Solving for variable 'x'. Combine like terms: 2x + 40x = 42x -9 + 42x + 40x2 = -40x + -40x2 + 40x + 40x2 Reorder the terms: -9 + 42x + 40x2 = -40x + 40x + -40x2 + 40x2 Combine like terms: -40x + 40x = 0 -9 + 42x + 40x2 = 0 + -40x2 + 40x2 -9 + 42x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 -9 + 42x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.225 + 1.05x + x2 = 0 Move the constant term to the right: Add '0.225' to each side of the equation. -0.225 + 1.05x + 0.225 + x2 = 0 + 0.225 Reorder the terms: -0.225 + 0.225 + 1.05x + x2 = 0 + 0.225 Combine like terms: -0.225 + 0.225 = 0.000 0.000 + 1.05x + x2 = 0 + 0.225 1.05x + x2 = 0 + 0.225 Combine like terms: 0 + 0.225 = 0.225 1.05x + x2 = 0.225 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = 0.225 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = 0.225 + 0.275625 Combine like terms: 0.225 + 0.275625 = 0.500625 0.275625 + 1.05x + x2 = 0.500625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 0.500625 Calculate the square root of the right side: 0.707548585 Break this problem into two subproblems by setting (x + 0.525) equal to 0.707548585 and -0.707548585.Subproblem 1
x + 0.525 = 0.707548585 Simplifying x + 0.525 = 0.707548585 Reorder the terms: 0.525 + x = 0.707548585 Solving 0.525 + x = 0.707548585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 0.707548585 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 0.707548585 + -0.525 x = 0.707548585 + -0.525 Combine like terms: 0.707548585 + -0.525 = 0.182548585 x = 0.182548585 Simplifying x = 0.182548585Subproblem 2
x + 0.525 = -0.707548585 Simplifying x + 0.525 = -0.707548585 Reorder the terms: 0.525 + x = -0.707548585 Solving 0.525 + x = -0.707548585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -0.707548585 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -0.707548585 + -0.525 x = -0.707548585 + -0.525 Combine like terms: -0.707548585 + -0.525 = -1.232548585 x = -1.232548585 Simplifying x = -1.232548585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.182548585, -1.232548585}
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