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Simplifying 3x(x + -5) = 14 Reorder the terms: 3x(-5 + x) = 14 (-5 * 3x + x * 3x) = 14 (-15x + 3x2) = 14 Solving -15x + 3x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -15x + 3x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -5x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -5x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 4.666666667 -5x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -5x + x2 = 4.666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 4.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4.666666667 + 6.25 Combine like terms: 4.666666667 + 6.25 = 10.916666667 6.25 + -5x + x2 = 10.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.916666667 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (x + -2.5) equal to 3.304037934 and -3.304037934.Subproblem 1
x + -2.5 = 3.304037934 Simplifying x + -2.5 = 3.304037934 Reorder the terms: -2.5 + x = 3.304037934 Solving -2.5 + x = 3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.304037934 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.304037934 + 2.5 x = 3.304037934 + 2.5 Combine like terms: 3.304037934 + 2.5 = 5.804037934 x = 5.804037934 Simplifying x = 5.804037934Subproblem 2
x + -2.5 = -3.304037934 Simplifying x + -2.5 = -3.304037934 Reorder the terms: -2.5 + x = -3.304037934 Solving -2.5 + x = -3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.304037934 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.304037934 + 2.5 x = -3.304037934 + 2.5 Combine like terms: -3.304037934 + 2.5 = -0.804037934 x = -0.804037934 Simplifying x = -0.804037934Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.804037934, -0.804037934}
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