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Simplifying (180 + -6x + 14)(9 + 11x) + 50 = 180 Reorder the terms: (180 + 14 + -6x)(9 + 11x) + 50 = 180 Combine like terms: 180 + 14 = 194 (194 + -6x)(9 + 11x) + 50 = 180 Multiply (194 + -6x) * (9 + 11x) (194(9 + 11x) + -6x * (9 + 11x)) + 50 = 180 ((9 * 194 + 11x * 194) + -6x * (9 + 11x)) + 50 = 180 ((1746 + 2134x) + -6x * (9 + 11x)) + 50 = 180 (1746 + 2134x + (9 * -6x + 11x * -6x)) + 50 = 180 (1746 + 2134x + (-54x + -66x2)) + 50 = 180 Combine like terms: 2134x + -54x = 2080x (1746 + 2080x + -66x2) + 50 = 180 Reorder the terms: 1746 + 50 + 2080x + -66x2 = 180 Combine like terms: 1746 + 50 = 1796 1796 + 2080x + -66x2 = 180 Solving 1796 + 2080x + -66x2 = 180 Solving for variable 'x'. Reorder the terms: 1796 + -180 + 2080x + -66x2 = 180 + -180 Combine like terms: 1796 + -180 = 1616 1616 + 2080x + -66x2 = 180 + -180 Combine like terms: 180 + -180 = 0 1616 + 2080x + -66x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(808 + 1040x + -33x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(808 + 1040x + -33x2)' equal to zero and attempt to solve: Simplifying 808 + 1040x + -33x2 = 0 Solving 808 + 1040x + -33x2 = 0 Begin completing the square. Divide all terms by -33 the coefficient of the squared term: Divide each side by '-33'. -24.48484848 + -31.51515152x + x2 = 0 Move the constant term to the right: Add '24.48484848' to each side of the equation. -24.48484848 + -31.51515152x + 24.48484848 + x2 = 0 + 24.48484848 Reorder the terms: -24.48484848 + 24.48484848 + -31.51515152x + x2 = 0 + 24.48484848 Combine like terms: -24.48484848 + 24.48484848 = 0.00000000 0.00000000 + -31.51515152x + x2 = 0 + 24.48484848 -31.51515152x + x2 = 0 + 24.48484848 Combine like terms: 0 + 24.48484848 = 24.48484848 -31.51515152x + x2 = 24.48484848 The x term is -31.51515152x. Take half its coefficient (-15.75757576). Square it (248.3011938) and add it to both sides. Add '248.3011938' to each side of the equation. -31.51515152x + 248.3011938 + x2 = 24.48484848 + 248.3011938 Reorder the terms: 248.3011938 + -31.51515152x + x2 = 24.48484848 + 248.3011938 Combine like terms: 24.48484848 + 248.3011938 = 272.78604228 248.3011938 + -31.51515152x + x2 = 272.78604228 Factor a perfect square on the left side: (x + -15.75757576)(x + -15.75757576) = 272.78604228 Calculate the square root of the right side: 16.516235718 Break this problem into two subproblems by setting (x + -15.75757576) equal to 16.516235718 and -16.516235718.Subproblem 1
x + -15.75757576 = 16.516235718 Simplifying x + -15.75757576 = 16.516235718 Reorder the terms: -15.75757576 + x = 16.516235718 Solving -15.75757576 + x = 16.516235718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75757576' to each side of the equation. -15.75757576 + 15.75757576 + x = 16.516235718 + 15.75757576 Combine like terms: -15.75757576 + 15.75757576 = 0.00000000 0.00000000 + x = 16.516235718 + 15.75757576 x = 16.516235718 + 15.75757576 Combine like terms: 16.516235718 + 15.75757576 = 32.273811478 x = 32.273811478 Simplifying x = 32.273811478Subproblem 2
x + -15.75757576 = -16.516235718 Simplifying x + -15.75757576 = -16.516235718 Reorder the terms: -15.75757576 + x = -16.516235718 Solving -15.75757576 + x = -16.516235718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75757576' to each side of the equation. -15.75757576 + 15.75757576 + x = -16.516235718 + 15.75757576 Combine like terms: -15.75757576 + 15.75757576 = 0.00000000 0.00000000 + x = -16.516235718 + 15.75757576 x = -16.516235718 + 15.75757576 Combine like terms: -16.516235718 + 15.75757576 = -0.758659958 x = -0.758659958 Simplifying x = -0.758659958Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.273811478, -0.758659958}Solution
x = {32.273811478, -0.758659958}
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