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Simplifying (4x * 4x + -4x + 11) + (8x * 8x + 7x + -53) = 0 Reorder the terms for easier multiplication: (4 * 4x * x + -4x + 11) + (8x * 8x + 7x + -53) = 0 Multiply 4 * 4 (16x * x + -4x + 11) + (8x * 8x + 7x + -53) = 0 Multiply x * x (16x2 + -4x + 11) + (8x * 8x + 7x + -53) = 0 Reorder the terms: (11 + -4x + 16x2) + (8x * 8x + 7x + -53) = 0 Remove parenthesis around (11 + -4x + 16x2) 11 + -4x + 16x2 + (8x * 8x + 7x + -53) = 0 Reorder the terms for easier multiplication: 11 + -4x + 16x2 + (8 * 8x * x + 7x + -53) = 0 Multiply 8 * 8 11 + -4x + 16x2 + (64x * x + 7x + -53) = 0 Multiply x * x 11 + -4x + 16x2 + (64x2 + 7x + -53) = 0 Reorder the terms: 11 + -4x + 16x2 + (-53 + 7x + 64x2) = 0 Remove parenthesis around (-53 + 7x + 64x2) 11 + -4x + 16x2 + -53 + 7x + 64x2 = 0 Reorder the terms: 11 + -53 + -4x + 7x + 16x2 + 64x2 = 0 Combine like terms: 11 + -53 = -42 -42 + -4x + 7x + 16x2 + 64x2 = 0 Combine like terms: -4x + 7x = 3x -42 + 3x + 16x2 + 64x2 = 0 Combine like terms: 16x2 + 64x2 = 80x2 -42 + 3x + 80x2 = 0 Solving -42 + 3x + 80x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -0.525 + 0.0375x + x2 = 0.0 Move the constant term to the right: Add '0.525' to each side of the equation. -0.525 + 0.0375x + 0.525 + x2 = 0.0 + 0.525 Reorder the terms: -0.525 + 0.525 + 0.0375x + x2 = 0.0 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + 0.0375x + x2 = 0.0 + 0.525 0.0375x + x2 = 0.0 + 0.525 Combine like terms: 0.0 + 0.525 = 0.525 0.0375x + x2 = 0.525 The x term is 0.0375x. Take half its coefficient (0.01875). Square it (0.0003515625) and add it to both sides. Add '0.0003515625' to each side of the equation. 0.0375x + 0.0003515625 + x2 = 0.525 + 0.0003515625 Reorder the terms: 0.0003515625 + 0.0375x + x2 = 0.525 + 0.0003515625 Combine like terms: 0.525 + 0.0003515625 = 0.5253515625 0.0003515625 + 0.0375x + x2 = 0.5253515625 Factor a perfect square on the left side: (x + 0.01875)(x + 0.01875) = 0.5253515625 Calculate the square root of the right side: 0.724811398 Break this problem into two subproblems by setting (x + 0.01875) equal to 0.724811398 and -0.724811398.Subproblem 1
x + 0.01875 = 0.724811398 Simplifying x + 0.01875 = 0.724811398 Reorder the terms: 0.01875 + x = 0.724811398 Solving 0.01875 + x = 0.724811398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01875' to each side of the equation. 0.01875 + -0.01875 + x = 0.724811398 + -0.01875 Combine like terms: 0.01875 + -0.01875 = 0.00000 0.00000 + x = 0.724811398 + -0.01875 x = 0.724811398 + -0.01875 Combine like terms: 0.724811398 + -0.01875 = 0.706061398 x = 0.706061398 Simplifying x = 0.706061398Subproblem 2
x + 0.01875 = -0.724811398 Simplifying x + 0.01875 = -0.724811398 Reorder the terms: 0.01875 + x = -0.724811398 Solving 0.01875 + x = -0.724811398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01875' to each side of the equation. 0.01875 + -0.01875 + x = -0.724811398 + -0.01875 Combine like terms: 0.01875 + -0.01875 = 0.00000 0.00000 + x = -0.724811398 + -0.01875 x = -0.724811398 + -0.01875 Combine like terms: -0.724811398 + -0.01875 = -0.743561398 x = -0.743561398 Simplifying x = -0.743561398Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.706061398, -0.743561398}
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