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Simplifying 4x(4x) + -7x + 3 + 2x(2x) + 2x + -7 = 0 Remove parenthesis around (4x) 4x * 4x + -7x + 3 + 2x(2x) + 2x + -7 = 0 Reorder the terms for easier multiplication: 4 * 4x * x + -7x + 3 + 2x(2x) + 2x + -7 = 0 Multiply 4 * 4 16x * x + -7x + 3 + 2x(2x) + 2x + -7 = 0 Multiply x * x 16x2 + -7x + 3 + 2x(2x) + 2x + -7 = 0 Remove parenthesis around (2x) 16x2 + -7x + 3 + 2x * 2x + 2x + -7 = 0 Reorder the terms for easier multiplication: 16x2 + -7x + 3 + 2 * 2x * x + 2x + -7 = 0 Multiply 2 * 2 16x2 + -7x + 3 + 4x * x + 2x + -7 = 0 Multiply x * x 16x2 + -7x + 3 + 4x2 + 2x + -7 = 0 Reorder the terms: 3 + -7 + -7x + 2x + 16x2 + 4x2 = 0 Combine like terms: 3 + -7 = -4 -4 + -7x + 2x + 16x2 + 4x2 = 0 Combine like terms: -7x + 2x = -5x -4 + -5x + 16x2 + 4x2 = 0 Combine like terms: 16x2 + 4x2 = 20x2 -4 + -5x + 20x2 = 0 Solving -4 + -5x + 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'. -0.2 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.25x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.25x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.25x + x2 = 0.0 + 0.2 -0.25x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -0.25x + x2 = 0.2 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.2 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.2 + 0.015625 Combine like terms: 0.2 + 0.015625 = 0.215625 0.015625 + -0.25x + x2 = 0.215625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.215625 Calculate the square root of the right side: 0.464354391 Break this problem into two subproblems by setting (x + -0.125) equal to 0.464354391 and -0.464354391.Subproblem 1
x + -0.125 = 0.464354391 Simplifying x + -0.125 = 0.464354391 Reorder the terms: -0.125 + x = 0.464354391 Solving -0.125 + x = 0.464354391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.464354391 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.464354391 + 0.125 x = 0.464354391 + 0.125 Combine like terms: 0.464354391 + 0.125 = 0.589354391 x = 0.589354391 Simplifying x = 0.589354391Subproblem 2
x + -0.125 = -0.464354391 Simplifying x + -0.125 = -0.464354391 Reorder the terms: -0.125 + x = -0.464354391 Solving -0.125 + x = -0.464354391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.464354391 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.464354391 + 0.125 x = -0.464354391 + 0.125 Combine like terms: -0.464354391 + 0.125 = -0.339354391 x = -0.339354391 Simplifying x = -0.339354391Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.589354391, -0.339354391}
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