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Simplifying 14x(-3x + 5) = 3 Reorder the terms: 14x(5 + -3x) = 3 (5 * 14x + -3x * 14x) = 3 (70x + -42x2) = 3 Solving 70x + -42x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 70x + -42x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 70x + -42x2 = 0 Begin completing the square. Divide all terms by -42 the coefficient of the squared term: Divide each side by '-42'. 0.07142857143 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -1.666666667x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -1.666666667x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -1.666666667x + x2 = 0 + -0.07142857143 -1.666666667x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -1.666666667x + x2 = -0.07142857143 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -0.07142857143 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.07142857143 + 0.6944444447 Combine like terms: -0.07142857143 + 0.6944444447 = 0.62301587327 0.6944444447 + -1.666666667x + x2 = 0.62301587327 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.62301587327 Calculate the square root of the right side: 0.789313546 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.789313546 and -0.789313546.Subproblem 1
x + -0.8333333335 = 0.789313546 Simplifying x + -0.8333333335 = 0.789313546 Reorder the terms: -0.8333333335 + x = 0.789313546 Solving -0.8333333335 + x = 0.789313546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.789313546 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.789313546 + 0.8333333335 x = 0.789313546 + 0.8333333335 Combine like terms: 0.789313546 + 0.8333333335 = 1.6226468795 x = 1.6226468795 Simplifying x = 1.6226468795Subproblem 2
x + -0.8333333335 = -0.789313546 Simplifying x + -0.8333333335 = -0.789313546 Reorder the terms: -0.8333333335 + x = -0.789313546 Solving -0.8333333335 + x = -0.789313546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.789313546 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.789313546 + 0.8333333335 x = -0.789313546 + 0.8333333335 Combine like terms: -0.789313546 + 0.8333333335 = 0.0440197875 x = 0.0440197875 Simplifying x = 0.0440197875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6226468795, 0.0440197875}
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