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Simplifying 3x2 = 15x + -5 Reorder the terms: 3x2 = -5 + 15x Solving 3x2 = -5 + 15x Solving for variable 'x'. Reorder the terms: 5 + -15x + 3x2 = -5 + 15x + 5 + -15x Reorder the terms: 5 + -15x + 3x2 = -5 + 5 + 15x + -15x Combine like terms: -5 + 5 = 0 5 + -15x + 3x2 = 0 + 15x + -15x 5 + -15x + 3x2 = 15x + -15x Combine like terms: 15x + -15x = 0 5 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -5x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -5x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + -1.666666667 -5x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -5x + x2 = -1.666666667 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 = -1.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.666666667 + 6.25 Combine like terms: -1.666666667 + 6.25 = 4.583333333 6.25 + -5x + x2 = 4.583333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.583333333 Calculate the square root of the right side: 2.140872096 Break this problem into two subproblems by setting (x + -2.5) equal to 2.140872096 and -2.140872096.Subproblem 1
x + -2.5 = 2.140872096 Simplifying x + -2.5 = 2.140872096 Reorder the terms: -2.5 + x = 2.140872096 Solving -2.5 + x = 2.140872096 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 = 2.140872096 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.140872096 + 2.5 x = 2.140872096 + 2.5 Combine like terms: 2.140872096 + 2.5 = 4.640872096 x = 4.640872096 Simplifying x = 4.640872096Subproblem 2
x + -2.5 = -2.140872096 Simplifying x + -2.5 = -2.140872096 Reorder the terms: -2.5 + x = -2.140872096 Solving -2.5 + x = -2.140872096 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 = -2.140872096 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.140872096 + 2.5 x = -2.140872096 + 2.5 Combine like terms: -2.140872096 + 2.5 = 0.359127904 x = 0.359127904 Simplifying x = 0.359127904Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.640872096, 0.359127904}
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