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Simplifying (0.1x + 0.3)(0.4x + -20) = 0 Reorder the terms: (0.3 + 0.1x)(0.4x + -20) = 0 Reorder the terms: (0.3 + 0.1x)(-20 + 0.4x) = 0 Multiply (0.3 + 0.1x) * (-20 + 0.4x) (0.3(-20 + 0.4x) + 0.1x * (-20 + 0.4x)) = 0 ((-20 * 0.3 + 0.4x * 0.3) + 0.1x * (-20 + 0.4x)) = 0 ((-6 + 0.12x) + 0.1x * (-20 + 0.4x)) = 0 (-6 + 0.12x + (-20 * 0.1x + 0.4x * 0.1x)) = 0 (-6 + 0.12x + (-2x + 0.04x2)) = 0 Combine like terms: 0.12x + -2x = -1.88x (-6 + -1.88x + 0.04x2) = 0 Solving -6 + -1.88x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -150 + -47x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -47x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -47x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -47x + x2 = 0 + 150 -47x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -47x + x2 = 150 The x term is -47x. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47x + 552.25 + x2 = 150 + 552.25 Reorder the terms: 552.25 + -47x + x2 = 150 + 552.25 Combine like terms: 150 + 552.25 = 702.25 552.25 + -47x + x2 = 702.25 Factor a perfect square on the left side: (x + -23.5)(x + -23.5) = 702.25 Calculate the square root of the right side: 26.5 Break this problem into two subproblems by setting (x + -23.5) equal to 26.5 and -26.5.Subproblem 1
x + -23.5 = 26.5 Simplifying x + -23.5 = 26.5 Reorder the terms: -23.5 + x = 26.5 Solving -23.5 + x = 26.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = 26.5 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = 26.5 + 23.5 x = 26.5 + 23.5 Combine like terms: 26.5 + 23.5 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -23.5 = -26.5 Simplifying x + -23.5 = -26.5 Reorder the terms: -23.5 + x = -26.5 Solving -23.5 + x = -26.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = -26.5 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = -26.5 + 23.5 x = -26.5 + 23.5 Combine like terms: -26.5 + 23.5 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -3}
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