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Simplifying (3x + -16) * 6.2x = -14 Reorder the terms: (-16 + 3x) * 6.2x = -14 Reorder the terms for easier multiplication: 6.2x(-16 + 3x) = -14 (-16 * 6.2x + 3x * 6.2x) = -14 (-99.2x + 18.6x2) = -14 Solving -99.2x + 18.6x2 = -14 Solving for variable 'x'. Reorder the terms: 14 + -99.2x + 18.6x2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + -99.2x + 18.6x2 = 0 Begin completing the square. Divide all terms by 18.6 the coefficient of the squared term: Divide each side by '18.6'. 0.752688172 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-0.752688172' to each side of the equation. 0.752688172 + -5.333333333x + -0.752688172 + x2 = 0 + -0.752688172 Reorder the terms: 0.752688172 + -0.752688172 + -5.333333333x + x2 = 0 + -0.752688172 Combine like terms: 0.752688172 + -0.752688172 = 0.000000000 0.000000000 + -5.333333333x + x2 = 0 + -0.752688172 -5.333333333x + x2 = 0 + -0.752688172 Combine like terms: 0 + -0.752688172 = -0.752688172 -5.333333333x + x2 = -0.752688172 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 = -0.752688172 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -0.752688172 + 7.111111113 Combine like terms: -0.752688172 + 7.111111113 = 6.358422941 7.111111113 + -5.333333333x + x2 = 6.358422941 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 6.358422941 Calculate the square root of the right side: 2.521591351 Break this problem into two subproblems by setting (x + -2.666666667) equal to 2.521591351 and -2.521591351.Subproblem 1
x + -2.666666667 = 2.521591351 Simplifying x + -2.666666667 = 2.521591351 Reorder the terms: -2.666666667 + x = 2.521591351 Solving -2.666666667 + x = 2.521591351 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 = 2.521591351 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 2.521591351 + 2.666666667 x = 2.521591351 + 2.666666667 Combine like terms: 2.521591351 + 2.666666667 = 5.188258018 x = 5.188258018 Simplifying x = 5.188258018Subproblem 2
x + -2.666666667 = -2.521591351 Simplifying x + -2.666666667 = -2.521591351 Reorder the terms: -2.666666667 + x = -2.521591351 Solving -2.666666667 + x = -2.521591351 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 = -2.521591351 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -2.521591351 + 2.666666667 x = -2.521591351 + 2.666666667 Combine like terms: -2.521591351 + 2.666666667 = 0.145075316 x = 0.145075316 Simplifying x = 0.145075316Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.188258018, 0.145075316}
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