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Simplifying 3x2 + -7x + -23 = 7 Reorder the terms: -23 + -7x + 3x2 = 7 Solving -23 + -7x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: -23 + -7 + -7x + 3x2 = 7 + -7 Combine like terms: -23 + -7 = -30 -30 + -7x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -30 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2.333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2.333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2.333333333x + x2 = 0 + 10 -2.333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2.333333333x + x2 = 10 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 = 10 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 10 + 1.361111112 Combine like terms: 10 + 1.361111112 = 11.361111112 1.361111112 + -2.333333333x + x2 = 11.361111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 11.361111112 Calculate the square root of the right side: 3.370624736 Break this problem into two subproblems by setting (x + -1.166666667) equal to 3.370624736 and -3.370624736.Subproblem 1
x + -1.166666667 = 3.370624736 Simplifying x + -1.166666667 = 3.370624736 Reorder the terms: -1.166666667 + x = 3.370624736 Solving -1.166666667 + x = 3.370624736 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 = 3.370624736 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 3.370624736 + 1.166666667 x = 3.370624736 + 1.166666667 Combine like terms: 3.370624736 + 1.166666667 = 4.537291403 x = 4.537291403 Simplifying x = 4.537291403Subproblem 2
x + -1.166666667 = -3.370624736 Simplifying x + -1.166666667 = -3.370624736 Reorder the terms: -1.166666667 + x = -3.370624736 Solving -1.166666667 + x = -3.370624736 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 = -3.370624736 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -3.370624736 + 1.166666667 x = -3.370624736 + 1.166666667 Combine like terms: -3.370624736 + 1.166666667 = -2.203958069 x = -2.203958069 Simplifying x = -2.203958069Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.537291403, -2.203958069}
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