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Simplifying (6.2x + 9.3)(4x + -3.6) = 0 Reorder the terms: (9.3 + 6.2x)(4x + -3.6) = 0 Reorder the terms: (9.3 + 6.2x)(-3.6 + 4x) = 0 Multiply (9.3 + 6.2x) * (-3.6 + 4x) (9.3(-3.6 + 4x) + 6.2x * (-3.6 + 4x)) = 0 ((-3.6 * 9.3 + 4x * 9.3) + 6.2x * (-3.6 + 4x)) = 0 ((-33.48 + 37.2x) + 6.2x * (-3.6 + 4x)) = 0 (-33.48 + 37.2x + (-3.6 * 6.2x + 4x * 6.2x)) = 0 (-33.48 + 37.2x + (-22.32x + 24.8x2)) = 0 Combine like terms: 37.2x + -22.32x = 14.88x (-33.48 + 14.88x + 24.8x2) = 0 Solving -33.48 + 14.88x + 24.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24.8 the coefficient of the squared term: Divide each side by '24.8'. -1.35 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.35' to each side of the equation. -1.35 + 0.6x + 1.35 + x2 = 0 + 1.35 Reorder the terms: -1.35 + 1.35 + 0.6x + x2 = 0 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + 0.6x + x2 = 0 + 1.35 0.6x + x2 = 0 + 1.35 Combine like terms: 0 + 1.35 = 1.35 0.6x + x2 = 1.35 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.35 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.35 + 0.09 Combine like terms: 1.35 + 0.09 = 1.44 0.09 + 0.6x + x2 = 1.44 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.44 Calculate the square root of the right side: 1.2 Break this problem into two subproblems by setting (x + 0.3) equal to 1.2 and -1.2.Subproblem 1
x + 0.3 = 1.2 Simplifying x + 0.3 = 1.2 Reorder the terms: 0.3 + x = 1.2 Solving 0.3 + x = 1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.2 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.2 + -0.3 x = 1.2 + -0.3 Combine like terms: 1.2 + -0.3 = 0.9 x = 0.9 Simplifying x = 0.9Subproblem 2
x + 0.3 = -1.2 Simplifying x + 0.3 = -1.2 Reorder the terms: 0.3 + x = -1.2 Solving 0.3 + x = -1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.2 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.2 + -0.3 x = -1.2 + -0.3 Combine like terms: -1.2 + -0.3 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9, -1.5}
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