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Simplifying (0.3x + -1.25)(15x + 5) = 0 Reorder the terms: (-1.25 + 0.3x)(15x + 5) = 0 Reorder the terms: (-1.25 + 0.3x)(5 + 15x) = 0 Multiply (-1.25 + 0.3x) * (5 + 15x) (-1.25(5 + 15x) + 0.3x * (5 + 15x)) = 0 ((5 * -1.25 + 15x * -1.25) + 0.3x * (5 + 15x)) = 0 ((-6.25 + -18.75x) + 0.3x * (5 + 15x)) = 0 (-6.25 + -18.75x + (5 * 0.3x + 15x * 0.3x)) = 0 (-6.25 + -18.75x + (1.5x + 4.5x2)) = 0 Combine like terms: -18.75x + 1.5x = -17.25x (-6.25 + -17.25x + 4.5x2) = 0 Solving -6.25 + -17.25x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. -1.388888889 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '1.388888889' to each side of the equation. -1.388888889 + -3.833333333x + 1.388888889 + x2 = 0 + 1.388888889 Reorder the terms: -1.388888889 + 1.388888889 + -3.833333333x + x2 = 0 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + -3.833333333x + x2 = 0 + 1.388888889 -3.833333333x + x2 = 0 + 1.388888889 Combine like terms: 0 + 1.388888889 = 1.388888889 -3.833333333x + x2 = 1.388888889 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = 1.388888889 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = 1.388888889 + 3.673611112 Combine like terms: 1.388888889 + 3.673611112 = 5.062500001 3.673611112 + -3.833333333x + x2 = 5.062500001 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 5.062500001 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -1.916666667) equal to 2.25 and -2.25.Subproblem 1
x + -1.916666667 = 2.25 Simplifying x + -1.916666667 = 2.25 Reorder the terms: -1.916666667 + x = 2.25 Solving -1.916666667 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 2.25 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 2.25 + 1.916666667 x = 2.25 + 1.916666667 Combine like terms: 2.25 + 1.916666667 = 4.166666667 x = 4.166666667 Simplifying x = 4.166666667Subproblem 2
x + -1.916666667 = -2.25 Simplifying x + -1.916666667 = -2.25 Reorder the terms: -1.916666667 + x = -2.25 Solving -1.916666667 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -2.25 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -2.25 + 1.916666667 x = -2.25 + 1.916666667 Combine like terms: -2.25 + 1.916666667 = -0.333333333 x = -0.333333333 Simplifying x = -0.333333333Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.166666667, -0.333333333}
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