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Simplifying 3x2 + 15x + 17 = 0 Reorder the terms: 17 + 15x + 3x2 = 0 Solving 17 + 15x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + 5x + x2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + 5x + -5.666666667 + x2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + 5x + x2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + 5x + x2 = 0 + -5.666666667 5x + x2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 5x + x2 = -5.666666667 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 = -5.666666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -5.666666667 + 6.25 Combine like terms: -5.666666667 + 6.25 = 0.583333333 6.25 + 5x + x2 = 0.583333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 0.583333333 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (x + 2.5) equal to 0.763762616 and -0.763762616.Subproblem 1
x + 2.5 = 0.763762616 Simplifying x + 2.5 = 0.763762616 Reorder the terms: 2.5 + x = 0.763762616 Solving 2.5 + x = 0.763762616 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 = 0.763762616 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.763762616 + -2.5 x = 0.763762616 + -2.5 Combine like terms: 0.763762616 + -2.5 = -1.736237384 x = -1.736237384 Simplifying x = -1.736237384Subproblem 2
x + 2.5 = -0.763762616 Simplifying x + 2.5 = -0.763762616 Reorder the terms: 2.5 + x = -0.763762616 Solving 2.5 + x = -0.763762616 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 = -0.763762616 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -0.763762616 + -2.5 x = -0.763762616 + -2.5 Combine like terms: -0.763762616 + -2.5 = -3.263762616 x = -3.263762616 Simplifying x = -3.263762616Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.736237384, -3.263762616}
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