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Simplifying 3x(5 + -4x) + 5 = 2x (5 * 3x + -4x * 3x) + 5 = 2x (15x + -12x2) + 5 = 2x Reorder the terms: 5 + 15x + -12x2 = 2x Solving 5 + 15x + -12x2 = 2x Solving for variable 'x'. Reorder the terms: 5 + 15x + -2x + -12x2 = 2x + -2x Combine like terms: 15x + -2x = 13x 5 + 13x + -12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 5 + 13x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.4166666667 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -1.083333333x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -1.083333333x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -1.083333333x + x2 = 0 + 0.4166666667 -1.083333333x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -1.083333333x + x2 = 0.4166666667 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = 0.4166666667 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 0.4166666667 + 0.2934027776 Combine like terms: 0.4166666667 + 0.2934027776 = 0.7100694443 0.2934027776 + -1.083333333x + x2 = 0.7100694443 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 0.7100694443 Calculate the square root of the right side: 0.842656184 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 0.842656184 and -0.842656184.Subproblem 1
x + -0.5416666665 = 0.842656184 Simplifying x + -0.5416666665 = 0.842656184 Reorder the terms: -0.5416666665 + x = 0.842656184 Solving -0.5416666665 + x = 0.842656184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = 0.842656184 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 0.842656184 + 0.5416666665 x = 0.842656184 + 0.5416666665 Combine like terms: 0.842656184 + 0.5416666665 = 1.3843228505 x = 1.3843228505 Simplifying x = 1.3843228505Subproblem 2
x + -0.5416666665 = -0.842656184 Simplifying x + -0.5416666665 = -0.842656184 Reorder the terms: -0.5416666665 + x = -0.842656184 Solving -0.5416666665 + x = -0.842656184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = -0.842656184 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -0.842656184 + 0.5416666665 x = -0.842656184 + 0.5416666665 Combine like terms: -0.842656184 + 0.5416666665 = -0.3009895175 x = -0.3009895175 Simplifying x = -0.3009895175Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3843228505, -0.3009895175}
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