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Simplifying (4x * 4x + -6x + 16) + (2x * 2x + 9x + -66) = 0 Reorder the terms for easier multiplication: (4 * 4x * x + -6x + 16) + (2x * 2x + 9x + -66) = 0 Multiply 4 * 4 (16x * x + -6x + 16) + (2x * 2x + 9x + -66) = 0 Multiply x * x (16x2 + -6x + 16) + (2x * 2x + 9x + -66) = 0 Reorder the terms: (16 + -6x + 16x2) + (2x * 2x + 9x + -66) = 0 Remove parenthesis around (16 + -6x + 16x2) 16 + -6x + 16x2 + (2x * 2x + 9x + -66) = 0 Reorder the terms for easier multiplication: 16 + -6x + 16x2 + (2 * 2x * x + 9x + -66) = 0 Multiply 2 * 2 16 + -6x + 16x2 + (4x * x + 9x + -66) = 0 Multiply x * x 16 + -6x + 16x2 + (4x2 + 9x + -66) = 0 Reorder the terms: 16 + -6x + 16x2 + (-66 + 9x + 4x2) = 0 Remove parenthesis around (-66 + 9x + 4x2) 16 + -6x + 16x2 + -66 + 9x + 4x2 = 0 Reorder the terms: 16 + -66 + -6x + 9x + 16x2 + 4x2 = 0 Combine like terms: 16 + -66 = -50 -50 + -6x + 9x + 16x2 + 4x2 = 0 Combine like terms: -6x + 9x = 3x -50 + 3x + 16x2 + 4x2 = 0 Combine like terms: 16x2 + 4x2 = 20x2 -50 + 3x + 20x2 = 0 Solving -50 + 3x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -2.5 + 0.15x + x2 = 0.0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.15x + 2.5 + x2 = 0.0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.15x + x2 = 0.0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.15x + x2 = 0.0 + 2.5 0.15x + x2 = 0.0 + 2.5 Combine like terms: 0.0 + 2.5 = 2.5 0.15x + x2 = 2.5 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 2.5 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 2.5 + 0.005625 Combine like terms: 2.5 + 0.005625 = 2.505625 0.005625 + 0.15x + x2 = 2.505625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 2.505625 Calculate the square root of the right side: 1.582916612 Break this problem into two subproblems by setting (x + 0.075) equal to 1.582916612 and -1.582916612.Subproblem 1
x + 0.075 = 1.582916612 Simplifying x + 0.075 = 1.582916612 Reorder the terms: 0.075 + x = 1.582916612 Solving 0.075 + x = 1.582916612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 1.582916612 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 1.582916612 + -0.075 x = 1.582916612 + -0.075 Combine like terms: 1.582916612 + -0.075 = 1.507916612 x = 1.507916612 Simplifying x = 1.507916612Subproblem 2
x + 0.075 = -1.582916612 Simplifying x + 0.075 = -1.582916612 Reorder the terms: 0.075 + x = -1.582916612 Solving 0.075 + x = -1.582916612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -1.582916612 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -1.582916612 + -0.075 x = -1.582916612 + -0.075 Combine like terms: -1.582916612 + -0.075 = -1.657916612 x = -1.657916612 Simplifying x = -1.657916612Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.507916612, -1.657916612}
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