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Simplifying 3x2 + 7x = 9 Reorder the terms: 7x + 3x2 = 9 Solving 7x + 3x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 7x + 3x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.333333333x + x2 = 0 + 3 2.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.333333333x + x2 = 3 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 = 3 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 3 + 1.361111112 Combine like terms: 3 + 1.361111112 = 4.361111112 1.361111112 + 2.333333333x + x2 = 4.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 4.361111112 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.088327348 and -2.088327348.Subproblem 1
x + 1.166666667 = 2.088327348 Simplifying x + 1.166666667 = 2.088327348 Reorder the terms: 1.166666667 + x = 2.088327348 Solving 1.166666667 + x = 2.088327348 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 = 2.088327348 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.088327348 + -1.166666667 x = 2.088327348 + -1.166666667 Combine like terms: 2.088327348 + -1.166666667 = 0.921660681 x = 0.921660681 Simplifying x = 0.921660681Subproblem 2
x + 1.166666667 = -2.088327348 Simplifying x + 1.166666667 = -2.088327348 Reorder the terms: 1.166666667 + x = -2.088327348 Solving 1.166666667 + x = -2.088327348 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 = -2.088327348 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.088327348 + -1.166666667 x = -2.088327348 + -1.166666667 Combine like terms: -2.088327348 + -1.166666667 = -3.254994015 x = -3.254994015 Simplifying x = -3.254994015Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.921660681, -3.254994015}
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