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Simplifying 7x(6x + 8) = -2 Reorder the terms: 7x(8 + 6x) = -2 (8 * 7x + 6x * 7x) = -2 (56x + 42x2) = -2 Solving 56x + 42x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 56x + 42x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 56x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 28x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 28x + 21x2)' equal to zero and attempt to solve: Simplifying 1 + 28x + 21x2 = 0 Solving 1 + 28x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + 1.333333333x + -0.04761904762 + x2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + 1.333333333x + x2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + 1.333333333x + x2 = 0 + -0.04761904762 1.333333333x + x2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 1.333333333x + x2 = -0.04761904762 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -0.04761904762 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.04761904762 + 0.4444444442 Combine like terms: -0.04761904762 + 0.4444444442 = 0.39682539658 0.4444444442 + 1.333333333x + x2 = 0.39682539658 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.39682539658 Calculate the square root of the right side: 0.629940788 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.629940788 and -0.629940788.Subproblem 1
x + 0.6666666665 = 0.629940788 Simplifying x + 0.6666666665 = 0.629940788 Reorder the terms: 0.6666666665 + x = 0.629940788 Solving 0.6666666665 + x = 0.629940788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.629940788 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.629940788 + -0.6666666665 x = 0.629940788 + -0.6666666665 Combine like terms: 0.629940788 + -0.6666666665 = -0.0367258785 x = -0.0367258785 Simplifying x = -0.0367258785Subproblem 2
x + 0.6666666665 = -0.629940788 Simplifying x + 0.6666666665 = -0.629940788 Reorder the terms: 0.6666666665 + x = -0.629940788 Solving 0.6666666665 + x = -0.629940788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.629940788 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.629940788 + -0.6666666665 x = -0.629940788 + -0.6666666665 Combine like terms: -0.629940788 + -0.6666666665 = -1.2966074545 x = -1.2966074545 Simplifying x = -1.2966074545Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0367258785, -1.2966074545}Solution
x = {-0.0367258785, -1.2966074545}
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