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Simplifying (2x + 0.4)(4x + -1.14) = 0 Reorder the terms: (0.4 + 2x)(4x + -1.14) = 0 Reorder the terms: (0.4 + 2x)(-1.14 + 4x) = 0 Multiply (0.4 + 2x) * (-1.14 + 4x) (0.4(-1.14 + 4x) + 2x * (-1.14 + 4x)) = 0 ((-1.14 * 0.4 + 4x * 0.4) + 2x * (-1.14 + 4x)) = 0 ((-0.456 + 1.6x) + 2x * (-1.14 + 4x)) = 0 (-0.456 + 1.6x + (-1.14 * 2x + 4x * 2x)) = 0 (-0.456 + 1.6x + (-2.28x + 8x2)) = 0 Combine like terms: 1.6x + -2.28x = -0.68x (-0.456 + -0.68x + 8x2) = 0 Solving -0.456 + -0.68x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.057 + -0.085x + x2 = 0 Move the constant term to the right: Add '0.057' to each side of the equation. -0.057 + -0.085x + 0.057 + x2 = 0 + 0.057 Reorder the terms: -0.057 + 0.057 + -0.085x + x2 = 0 + 0.057 Combine like terms: -0.057 + 0.057 = 0.000 0.000 + -0.085x + x2 = 0 + 0.057 -0.085x + x2 = 0 + 0.057 Combine like terms: 0 + 0.057 = 0.057 -0.085x + x2 = 0.057 The x term is -0.085x. Take half its coefficient (-0.0425). Square it (0.00180625) and add it to both sides. Add '0.00180625' to each side of the equation. -0.085x + 0.00180625 + x2 = 0.057 + 0.00180625 Reorder the terms: 0.00180625 + -0.085x + x2 = 0.057 + 0.00180625 Combine like terms: 0.057 + 0.00180625 = 0.05880625 0.00180625 + -0.085x + x2 = 0.05880625 Factor a perfect square on the left side: (x + -0.0425)(x + -0.0425) = 0.05880625 Calculate the square root of the right side: 0.2425 Break this problem into two subproblems by setting (x + -0.0425) equal to 0.2425 and -0.2425.Subproblem 1
x + -0.0425 = 0.2425 Simplifying x + -0.0425 = 0.2425 Reorder the terms: -0.0425 + x = 0.2425 Solving -0.0425 + x = 0.2425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0425' to each side of the equation. -0.0425 + 0.0425 + x = 0.2425 + 0.0425 Combine like terms: -0.0425 + 0.0425 = 0.0000 0.0000 + x = 0.2425 + 0.0425 x = 0.2425 + 0.0425 Combine like terms: 0.2425 + 0.0425 = 0.285 x = 0.285 Simplifying x = 0.285Subproblem 2
x + -0.0425 = -0.2425 Simplifying x + -0.0425 = -0.2425 Reorder the terms: -0.0425 + x = -0.2425 Solving -0.0425 + x = -0.2425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0425' to each side of the equation. -0.0425 + 0.0425 + x = -0.2425 + 0.0425 Combine like terms: -0.0425 + 0.0425 = 0.0000 0.0000 + x = -0.2425 + 0.0425 x = -0.2425 + 0.0425 Combine like terms: -0.2425 + 0.0425 = -0.2 x = -0.2 Simplifying x = -0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.285, -0.2}
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