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Simplifying 0 = 3x2 + -15x + -11 Reorder the terms: 0 = -11 + -15x + 3x2 Solving 0 = -11 + -15x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + 15x + -3x2 = -11 + -15x + 3x2 + 11 + 15x + -3x2 Reorder the terms: 11 + 15x + -3x2 = -11 + 11 + -15x + 15x + 3x2 + -3x2 Combine like terms: -11 + 11 = 0 11 + 15x + -3x2 = 0 + -15x + 15x + 3x2 + -3x2 11 + 15x + -3x2 = -15x + 15x + 3x2 + -3x2 Combine like terms: -15x + 15x = 0 11 + 15x + -3x2 = 0 + 3x2 + -3x2 11 + 15x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 11 + 15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -5x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -5x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 3.666666667 -5x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -5x + x2 = 3.666666667 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 = 3.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3.666666667 + 6.25 Combine like terms: 3.666666667 + 6.25 = 9.916666667 6.25 + -5x + x2 = 9.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.916666667 Calculate the square root of the right side: 3.149073938 Break this problem into two subproblems by setting (x + -2.5) equal to 3.149073938 and -3.149073938.Subproblem 1
x + -2.5 = 3.149073938 Simplifying x + -2.5 = 3.149073938 Reorder the terms: -2.5 + x = 3.149073938 Solving -2.5 + x = 3.149073938 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 = 3.149073938 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.149073938 + 2.5 x = 3.149073938 + 2.5 Combine like terms: 3.149073938 + 2.5 = 5.649073938 x = 5.649073938 Simplifying x = 5.649073938Subproblem 2
x + -2.5 = -3.149073938 Simplifying x + -2.5 = -3.149073938 Reorder the terms: -2.5 + x = -3.149073938 Solving -2.5 + x = -3.149073938 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 = -3.149073938 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.149073938 + 2.5 x = -3.149073938 + 2.5 Combine like terms: -3.149073938 + 2.5 = -0.649073938 x = -0.649073938 Simplifying x = -0.649073938Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.649073938, -0.649073938}
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