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Simplifying 5x + -3 = (x + 7) * 3x Reorder the terms: -3 + 5x = (x + 7) * 3x Reorder the terms: -3 + 5x = (7 + x) * 3x Reorder the terms for easier multiplication: -3 + 5x = 3x(7 + x) -3 + 5x = (7 * 3x + x * 3x) -3 + 5x = (21x + 3x2) Solving -3 + 5x = 21x + 3x2 Solving for variable 'x'. Combine like terms: 5x + -21x = -16x -3 + -16x + -3x2 = 21x + 3x2 + -21x + -3x2 Reorder the terms: -3 + -16x + -3x2 = 21x + -21x + 3x2 + -3x2 Combine like terms: 21x + -21x = 0 -3 + -16x + -3x2 = 0 + 3x2 + -3x2 -3 + -16x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -3 + -16x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 16x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 16x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 16x + 3x2 = 0 Solving 3 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 5.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5.333333333x + x2 = 0 + -1 5.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 5.333333333x + x2 = -1 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 = -1 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = -1 + 7.111111113 Combine like terms: -1 + 7.111111113 = 6.111111113 7.111111113 + 5.333333333x + x2 = 6.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 6.111111113 Calculate the square root of the right side: 2.472066163 Break this problem into two subproblems by setting (x + 2.666666667) equal to 2.472066163 and -2.472066163.Subproblem 1
x + 2.666666667 = 2.472066163 Simplifying x + 2.666666667 = 2.472066163 Reorder the terms: 2.666666667 + x = 2.472066163 Solving 2.666666667 + x = 2.472066163 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 = 2.472066163 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 2.472066163 + -2.666666667 x = 2.472066163 + -2.666666667 Combine like terms: 2.472066163 + -2.666666667 = -0.194600504 x = -0.194600504 Simplifying x = -0.194600504Subproblem 2
x + 2.666666667 = -2.472066163 Simplifying x + 2.666666667 = -2.472066163 Reorder the terms: 2.666666667 + x = -2.472066163 Solving 2.666666667 + x = -2.472066163 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 = -2.472066163 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -2.472066163 + -2.666666667 x = -2.472066163 + -2.666666667 Combine like terms: -2.472066163 + -2.666666667 = -5.13873283 x = -5.13873283 Simplifying x = -5.13873283Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.194600504, -5.13873283}Solution
x = {-0.194600504, -5.13873283}
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