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Simplifying -2(3x + 10) * 3x = 34 Reorder the terms: -2(10 + 3x) * 3x = 34 Reorder the terms for easier multiplication: -2 * 3x(10 + 3x) = 34 Multiply -2 * 3 -6x(10 + 3x) = 34 (10 * -6x + 3x * -6x) = 34 (-60x + -18x2) = 34 Solving -60x + -18x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + -60x + -18x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + -60x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(17 + 30x + 9x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(17 + 30x + 9x2)' equal to zero and attempt to solve: Simplifying 17 + 30x + 9x2 = 0 Solving 17 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.888888889 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.888888889' to each side of the equation. 1.888888889 + 3.333333333x + -1.888888889 + x2 = 0 + -1.888888889 Reorder the terms: 1.888888889 + -1.888888889 + 3.333333333x + x2 = 0 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -1.888888889 3.333333333x + x2 = 0 + -1.888888889 Combine like terms: 0 + -1.888888889 = -1.888888889 3.333333333x + x2 = -1.888888889 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -1.888888889 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -1.888888889 + 2.777777779 Combine like terms: -1.888888889 + 2.777777779 = 0.88888889 2.777777779 + 3.333333333x + x2 = 0.88888889 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 0.88888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (x + 1.666666667) equal to 0.942809042 and -0.942809042.Subproblem 1
x + 1.666666667 = 0.942809042 Simplifying x + 1.666666667 = 0.942809042 Reorder the terms: 1.666666667 + x = 0.942809042 Solving 1.666666667 + x = 0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 0.942809042 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 0.942809042 + -1.666666667 x = 0.942809042 + -1.666666667 Combine like terms: 0.942809042 + -1.666666667 = -0.723857625 x = -0.723857625 Simplifying x = -0.723857625Subproblem 2
x + 1.666666667 = -0.942809042 Simplifying x + 1.666666667 = -0.942809042 Reorder the terms: 1.666666667 + x = -0.942809042 Solving 1.666666667 + x = -0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -0.942809042 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -0.942809042 + -1.666666667 x = -0.942809042 + -1.666666667 Combine like terms: -0.942809042 + -1.666666667 = -2.609475709 x = -2.609475709 Simplifying x = -2.609475709Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.723857625, -2.609475709}Solution
x = {-0.723857625, -2.609475709}
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