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Simplifying (0.5x + -3)(0.6x + 3) = 0 Reorder the terms: (-3 + 0.5x)(0.6x + 3) = 0 Reorder the terms: (-3 + 0.5x)(3 + 0.6x) = 0 Multiply (-3 + 0.5x) * (3 + 0.6x) (-3(3 + 0.6x) + 0.5x * (3 + 0.6x)) = 0 ((3 * -3 + 0.6x * -3) + 0.5x * (3 + 0.6x)) = 0 ((-9 + -1.8x) + 0.5x * (3 + 0.6x)) = 0 (-9 + -1.8x + (3 * 0.5x + 0.6x * 0.5x)) = 0 (-9 + -1.8x + (1.5x + 0.3x2)) = 0 Combine like terms: -1.8x + 1.5x = -0.3x (-9 + -0.3x + 0.3x2) = 0 Solving -9 + -0.3x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -30 + -1x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -1x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -1x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1x + x2 = 0 + 30 -1x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -1x + x2 = 30 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 30 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 30 + 0.25 Combine like terms: 30 + 0.25 = 30.25 0.25 + -1x + x2 = 30.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + -0.5) equal to 5.5 and -5.5.Subproblem 1
x + -0.5 = 5.5 Simplifying x + -0.5 = 5.5 Reorder the terms: -0.5 + x = 5.5 Solving -0.5 + x = 5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.5 + 0.5 x = 5.5 + 0.5 Combine like terms: 5.5 + 0.5 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -0.5 = -5.5 Simplifying x + -0.5 = -5.5 Reorder the terms: -0.5 + x = -5.5 Solving -0.5 + x = -5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.5 + 0.5 x = -5.5 + 0.5 Combine like terms: -5.5 + 0.5 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -5}
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