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Simplifying 4x(10) * 2x + -2 = 3x + 4 Reorder the terms for easier multiplication: 4 * 10 * 2x * x + -2 = 3x + 4 Multiply 4 * 10 40 * 2x * x + -2 = 3x + 4 Multiply 40 * 2 80x * x + -2 = 3x + 4 Multiply x * x 80x2 + -2 = 3x + 4 Reorder the terms: -2 + 80x2 = 3x + 4 Reorder the terms: -2 + 80x2 = 4 + 3x Solving -2 + 80x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: -2 + -4 + -3x + 80x2 = 4 + 3x + -4 + -3x Combine like terms: -2 + -4 = -6 -6 + -3x + 80x2 = 4 + 3x + -4 + -3x Reorder the terms: -6 + -3x + 80x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 -6 + -3x + 80x2 = 0 + 3x + -3x -6 + -3x + 80x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -6 + -3x + 80x2 = 0 Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -0.075 + -0.0375x + x2 = 0.0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + -0.0375x + 0.075 + x2 = 0.0 + 0.075 Reorder the terms: -0.075 + 0.075 + -0.0375x + x2 = 0.0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + -0.0375x + x2 = 0.0 + 0.075 -0.0375x + x2 = 0.0 + 0.075 Combine like terms: 0.0 + 0.075 = 0.075 -0.0375x + x2 = 0.075 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 = 0.075 + 0.0003515625 Reorder the terms: 0.0003515625 + -0.0375x + x2 = 0.075 + 0.0003515625 Combine like terms: 0.075 + 0.0003515625 = 0.0753515625 0.0003515625 + -0.0375x + x2 = 0.0753515625 Factor a perfect square on the left side: (x + -0.01875)(x + -0.01875) = 0.0753515625 Calculate the square root of the right side: 0.274502391 Break this problem into two subproblems by setting (x + -0.01875) equal to 0.274502391 and -0.274502391.Subproblem 1
x + -0.01875 = 0.274502391 Simplifying x + -0.01875 = 0.274502391 Reorder the terms: -0.01875 + x = 0.274502391 Solving -0.01875 + x = 0.274502391 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 = 0.274502391 + 0.01875 Combine like terms: -0.01875 + 0.01875 = 0.00000 0.00000 + x = 0.274502391 + 0.01875 x = 0.274502391 + 0.01875 Combine like terms: 0.274502391 + 0.01875 = 0.293252391 x = 0.293252391 Simplifying x = 0.293252391Subproblem 2
x + -0.01875 = -0.274502391 Simplifying x + -0.01875 = -0.274502391 Reorder the terms: -0.01875 + x = -0.274502391 Solving -0.01875 + x = -0.274502391 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 = -0.274502391 + 0.01875 Combine like terms: -0.01875 + 0.01875 = 0.00000 0.00000 + x = -0.274502391 + 0.01875 x = -0.274502391 + 0.01875 Combine like terms: -0.274502391 + 0.01875 = -0.255752391 x = -0.255752391 Simplifying x = -0.255752391Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293252391, -0.255752391}
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