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Simplifying 3x2 + 7x + -15 = 0 Reorder the terms: -15 + 7x + 3x2 = 0 Solving -15 + 7x + 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 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.333333333x + x2 = 0 + 5 2.333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.333333333x + x2 = 5 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 5 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 5 + 1.361111112 Combine like terms: 5 + 1.361111112 = 6.361111112 1.361111112 + 2.333333333x + x2 = 6.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 6.361111112 Calculate the square root of the right side: 2.522124325 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.522124325 and -2.522124325.Subproblem 1
x + 1.166666667 = 2.522124325 Simplifying x + 1.166666667 = 2.522124325 Reorder the terms: 1.166666667 + x = 2.522124325 Solving 1.166666667 + x = 2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.522124325 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.522124325 + -1.166666667 x = 2.522124325 + -1.166666667 Combine like terms: 2.522124325 + -1.166666667 = 1.355457658 x = 1.355457658 Simplifying x = 1.355457658Subproblem 2
x + 1.166666667 = -2.522124325 Simplifying x + 1.166666667 = -2.522124325 Reorder the terms: 1.166666667 + x = -2.522124325 Solving 1.166666667 + x = -2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.522124325 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.522124325 + -1.166666667 x = -2.522124325 + -1.166666667 Combine like terms: -2.522124325 + -1.166666667 = -3.688790992 x = -3.688790992 Simplifying x = -3.688790992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.355457658, -3.688790992}
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