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Simplifying (6x * 6x) + -7x + -14 = 6 Reorder the terms for easier multiplication: (6 * 6x * x) + -7x + -14 = 6 Multiply 6 * 6 (36x * x) + -7x + -14 = 6 Multiply x * x (36x2) + -7x + -14 = 6 Reorder the terms: -14 + -7x + (36x2) = 6 Solving -14 + -7x + (36x2) = 6 Solving for variable 'x'. Reorder the terms: -14 + -6 + -7x + (36x2) = 6 + -6 Combine like terms: -14 + -6 = -20 -20 + -7x + (36x2) = 6 + -6 Combine like terms: 6 + -6 = 0 -20 + -7x + (36x2) = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.5555555556 + -0.1944444444x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.1944444444x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.1944444444x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.1944444444x + x2 = 0 + 0.5555555556 -0.1944444444x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.1944444444x + x2 = 0.5555555556 The x term is -0.1944444444x. Take half its coefficient (-0.0972222222). Square it (0.009452160490) and add it to both sides. Add '0.009452160490' to each side of the equation. -0.1944444444x + 0.009452160490 + x2 = 0.5555555556 + 0.009452160490 Reorder the terms: 0.009452160490 + -0.1944444444x + x2 = 0.5555555556 + 0.009452160490 Combine like terms: 0.5555555556 + 0.009452160490 = 0.56500771609 0.009452160490 + -0.1944444444x + x2 = 0.56500771609 Factor a perfect square on the left side: ((x) + -0.0972222222)((x) + -0.0972222222) = 0.56500771609 Calculate the square root of the right side: 0.751669952 Break this problem into two subproblems by setting ((x) + -0.0972222222) equal to 0.751669952 and -0.751669952.Subproblem 1
(x) + -0.0972222222 = 0.751669952 Simplifying (x) + -0.0972222222 = 0.751669952 x + -0.0972222222 = 0.751669952 Reorder the terms: -0.0972222222 + x = 0.751669952 Solving -0.0972222222 + x = 0.751669952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0972222222' to each side of the equation. -0.0972222222 + 0.0972222222 + x = 0.751669952 + 0.0972222222 Combine like terms: -0.0972222222 + 0.0972222222 = 0.0000000000 0.0000000000 + x = 0.751669952 + 0.0972222222 x = 0.751669952 + 0.0972222222 Combine like terms: 0.751669952 + 0.0972222222 = 0.8488921742 x = 0.8488921742 Simplifying x = 0.8488921742Subproblem 2
(x) + -0.0972222222 = -0.751669952 Simplifying (x) + -0.0972222222 = -0.751669952 x + -0.0972222222 = -0.751669952 Reorder the terms: -0.0972222222 + x = -0.751669952 Solving -0.0972222222 + x = -0.751669952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0972222222' to each side of the equation. -0.0972222222 + 0.0972222222 + x = -0.751669952 + 0.0972222222 Combine like terms: -0.0972222222 + 0.0972222222 = 0.0000000000 0.0000000000 + x = -0.751669952 + 0.0972222222 x = -0.751669952 + 0.0972222222 Combine like terms: -0.751669952 + 0.0972222222 = -0.6544477298 x = -0.6544477298 Simplifying x = -0.6544477298Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8488921742, -0.6544477298}
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