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Simplifying 3x2 + 5x + -15 = -6 Reorder the terms: -15 + 5x + 3x2 = -6 Solving -15 + 5x + 3x2 = -6 Solving for variable 'x'. Reorder the terms: -15 + 6 + 5x + 3x2 = -6 + 6 Combine like terms: -15 + 6 = -9 -9 + 5x + 3x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -9 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.666666667x + x2 = 0 + 3 1.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.666666667x + x2 = 3 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 3 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 3 + 0.6944444447 Combine like terms: 3 + 0.6944444447 = 3.6944444447 0.6944444447 + 1.666666667x + x2 = 3.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 3.6944444447 Calculate the square root of the right side: 1.922093766 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.922093766 and -1.922093766.Subproblem 1
x + 0.8333333335 = 1.922093766 Simplifying x + 0.8333333335 = 1.922093766 Reorder the terms: 0.8333333335 + x = 1.922093766 Solving 0.8333333335 + x = 1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.922093766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.922093766 + -0.8333333335 x = 1.922093766 + -0.8333333335 Combine like terms: 1.922093766 + -0.8333333335 = 1.0887604325 x = 1.0887604325 Simplifying x = 1.0887604325Subproblem 2
x + 0.8333333335 = -1.922093766 Simplifying x + 0.8333333335 = -1.922093766 Reorder the terms: 0.8333333335 + x = -1.922093766 Solving 0.8333333335 + x = -1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.922093766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.922093766 + -0.8333333335 x = -1.922093766 + -0.8333333335 Combine like terms: -1.922093766 + -0.8333333335 = -2.7554270995 x = -2.7554270995 Simplifying x = -2.7554270995Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0887604325, -2.7554270995}
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