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Simplifying 6[(-3) + -1x] * 2x = 14 6[-3 + -1x] * 2x = 14 Reorder the terms for easier multiplication: 6 * 2x[-3 + -1x] = 14 Multiply 6 * 2 12x[-3 + -1x] = 14 [-3 * 12x + -1x * 12x] = 14 [-36x + -12x2] = 14 Solving -36x + -12x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -36x + -12x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -36x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(7 + 18x + 6x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7 + 18x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + 18x + 6x2 = 0 Solving 7 + 18x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 3x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 3x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 3x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.166666667 3x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 3x + x2 = -1.166666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.166666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.166666667 + 2.25 Combine like terms: -1.166666667 + 2.25 = 1.083333333 2.25 + 3x + x2 = 1.083333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.083333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x + 1.5) equal to 1.040833 and -1.040833.Subproblem 1
x + 1.5 = 1.040833 Simplifying x + 1.5 = 1.040833 Reorder the terms: 1.5 + x = 1.040833 Solving 1.5 + x = 1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.040833 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.040833 + -1.5 x = 1.040833 + -1.5 Combine like terms: 1.040833 + -1.5 = -0.459167 x = -0.459167 Simplifying x = -0.459167Subproblem 2
x + 1.5 = -1.040833 Simplifying x + 1.5 = -1.040833 Reorder the terms: 1.5 + x = -1.040833 Solving 1.5 + x = -1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.040833 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.040833 + -1.5 x = -1.040833 + -1.5 Combine like terms: -1.040833 + -1.5 = -2.540833 x = -2.540833 Simplifying x = -2.540833Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.459167, -2.540833}Solution
x = {-0.459167, -2.540833}
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