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Simplifying (6x + 15)(6.4 + -0.8x) = 0 Reorder the terms: (15 + 6x)(6.4 + -0.8x) = 0 Multiply (15 + 6x) * (6.4 + -0.8x) (15(6.4 + -0.8x) + 6x * (6.4 + -0.8x)) = 0 ((6.4 * 15 + -0.8x * 15) + 6x * (6.4 + -0.8x)) = 0 ((96 + -12x) + 6x * (6.4 + -0.8x)) = 0 (96 + -12x + (6.4 * 6x + -0.8x * 6x)) = 0 (96 + -12x + (38.4x + -4.8x2)) = 0 Combine like terms: -12x + 38.4x = 26.4x (96 + 26.4x + -4.8x2) = 0 Solving 96 + 26.4x + -4.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.8 the coefficient of the squared term: Divide each side by '-4.8'. -20 + -5.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -5.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -5.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -5.5x + x2 = 0 + 20 -5.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -5.5x + x2 = 20 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 20 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 20 + 7.5625 Combine like terms: 20 + 7.5625 = 27.5625 7.5625 + -5.5x + x2 = 27.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 27.5625 Calculate the square root of the right side: 5.25 Break this problem into two subproblems by setting (x + -2.75) equal to 5.25 and -5.25.Subproblem 1
x + -2.75 = 5.25 Simplifying x + -2.75 = 5.25 Reorder the terms: -2.75 + x = 5.25 Solving -2.75 + x = 5.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 5.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 5.25 + 2.75 x = 5.25 + 2.75 Combine like terms: 5.25 + 2.75 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -2.75 = -5.25 Simplifying x + -2.75 = -5.25 Reorder the terms: -2.75 + x = -5.25 Solving -2.75 + x = -5.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -5.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -5.25 + 2.75 x = -5.25 + 2.75 Combine like terms: -5.25 + 2.75 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -2.5}
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