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Simplifying (3x + -70) * x = 180 Reorder the terms: (-70 + 3x) * x = 180 Reorder the terms for easier multiplication: x(-70 + 3x) = 180 (-70 * x + 3x * x) = 180 (-70x + 3x2) = 180 Solving -70x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -70x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -70x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + -23.33333333x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -23.33333333x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -23.33333333x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -23.33333333x + x2 = 0 + 60 -23.33333333x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -23.33333333x + x2 = 60 The x term is -23.33333333x. Take half its coefficient (-11.66666667). Square it (136.1111112) and add it to both sides. Add '136.1111112' to each side of the equation. -23.33333333x + 136.1111112 + x2 = 60 + 136.1111112 Reorder the terms: 136.1111112 + -23.33333333x + x2 = 60 + 136.1111112 Combine like terms: 60 + 136.1111112 = 196.1111112 136.1111112 + -23.33333333x + x2 = 196.1111112 Factor a perfect square on the left side: (x + -11.66666667)(x + -11.66666667) = 196.1111112 Calculate the square root of the right side: 14.003967695 Break this problem into two subproblems by setting (x + -11.66666667) equal to 14.003967695 and -14.003967695.Subproblem 1
x + -11.66666667 = 14.003967695 Simplifying x + -11.66666667 = 14.003967695 Reorder the terms: -11.66666667 + x = 14.003967695 Solving -11.66666667 + x = 14.003967695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = 14.003967695 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = 14.003967695 + 11.66666667 x = 14.003967695 + 11.66666667 Combine like terms: 14.003967695 + 11.66666667 = 25.670634365 x = 25.670634365 Simplifying x = 25.670634365Subproblem 2
x + -11.66666667 = -14.003967695 Simplifying x + -11.66666667 = -14.003967695 Reorder the terms: -11.66666667 + x = -14.003967695 Solving -11.66666667 + x = -14.003967695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = -14.003967695 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = -14.003967695 + 11.66666667 x = -14.003967695 + 11.66666667 Combine like terms: -14.003967695 + 11.66666667 = -2.337301025 x = -2.337301025 Simplifying x = -2.337301025Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.670634365, -2.337301025}
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