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Simplifying 2x(5 + 4x) = x + -1(2x + 2) (5 * 2x + 4x * 2x) = x + -1(2x + 2) (10x + 8x2) = x + -1(2x + 2) Reorder the terms: 10x + 8x2 = x + -1(2 + 2x) 10x + 8x2 = x + (2 * -1 + 2x * -1) 10x + 8x2 = x + (-2 + -2x) Reorder the terms: 10x + 8x2 = -2 + x + -2x Combine like terms: x + -2x = -1x 10x + 8x2 = -2 + -1x Solving 10x + 8x2 = -2 + -1x Solving for variable 'x'. Reorder the terms: 2 + 10x + x + 8x2 = -2 + -1x + 2 + x Combine like terms: 10x + x = 11x 2 + 11x + 8x2 = -2 + -1x + 2 + x Reorder the terms: 2 + 11x + 8x2 = -2 + 2 + -1x + x Combine like terms: -2 + 2 = 0 2 + 11x + 8x2 = 0 + -1x + x 2 + 11x + 8x2 = -1x + x Combine like terms: -1x + x = 0 2 + 11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 1.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.375x + x2 = 0 + -0.25 1.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.375x + x2 = -0.25 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = -0.25 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = -0.25 + 0.47265625 Combine like terms: -0.25 + 0.47265625 = 0.22265625 0.47265625 + 1.375x + x2 = 0.22265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + 0.6875) equal to 0.471864652 and -0.471864652.Subproblem 1
x + 0.6875 = 0.471864652 Simplifying x + 0.6875 = 0.471864652 Reorder the terms: 0.6875 + x = 0.471864652 Solving 0.6875 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 0.471864652 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 0.471864652 + -0.6875 x = 0.471864652 + -0.6875 Combine like terms: 0.471864652 + -0.6875 = -0.215635348 x = -0.215635348 Simplifying x = -0.215635348Subproblem 2
x + 0.6875 = -0.471864652 Simplifying x + 0.6875 = -0.471864652 Reorder the terms: 0.6875 + x = -0.471864652 Solving 0.6875 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -0.471864652 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -0.471864652 + -0.6875 x = -0.471864652 + -0.6875 Combine like terms: -0.471864652 + -0.6875 = -1.159364652 x = -1.159364652 Simplifying x = -1.159364652Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.215635348, -1.159364652}
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