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Simplifying 7x + 39 = 3x2 + 23x Reorder the terms: 39 + 7x = 3x2 + 23x Reorder the terms: 39 + 7x = 23x + 3x2 Solving 39 + 7x = 23x + 3x2 Solving for variable 'x'. Combine like terms: 7x + -23x = -16x 39 + -16x + -3x2 = 23x + 3x2 + -23x + -3x2 Reorder the terms: 39 + -16x + -3x2 = 23x + -23x + 3x2 + -3x2 Combine like terms: 23x + -23x = 0 39 + -16x + -3x2 = 0 + 3x2 + -3x2 39 + -16x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 39 + -16x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 5.333333333x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 5.333333333x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 5.333333333x + x2 = 0 + 13 5.333333333x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 5.333333333x + x2 = 13 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 13 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 13 + 7.111111113 Combine like terms: 13 + 7.111111113 = 20.111111113 7.111111113 + 5.333333333x + x2 = 20.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 20.111111113 Calculate the square root of the right side: 4.484541349 Break this problem into two subproblems by setting (x + 2.666666667) equal to 4.484541349 and -4.484541349.Subproblem 1
x + 2.666666667 = 4.484541349 Simplifying x + 2.666666667 = 4.484541349 Reorder the terms: 2.666666667 + x = 4.484541349 Solving 2.666666667 + x = 4.484541349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 4.484541349 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 4.484541349 + -2.666666667 x = 4.484541349 + -2.666666667 Combine like terms: 4.484541349 + -2.666666667 = 1.817874682 x = 1.817874682 Simplifying x = 1.817874682Subproblem 2
x + 2.666666667 = -4.484541349 Simplifying x + 2.666666667 = -4.484541349 Reorder the terms: 2.666666667 + x = -4.484541349 Solving 2.666666667 + x = -4.484541349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -4.484541349 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -4.484541349 + -2.666666667 x = -4.484541349 + -2.666666667 Combine like terms: -4.484541349 + -2.666666667 = -7.151208016 x = -7.151208016 Simplifying x = -7.151208016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.817874682, -7.151208016}
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