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Simplifying 7x(3x + -5) = -11 Reorder the terms: 7x(-5 + 3x) = -11 (-5 * 7x + 3x * 7x) = -11 (-35x + 21x2) = -11 Solving -35x + 21x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -35x + 21x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -35x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.5238095238 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.5238095238' to each side of the equation. 0.5238095238 + -1.666666667x + -0.5238095238 + x2 = 0 + -0.5238095238 Reorder the terms: 0.5238095238 + -0.5238095238 + -1.666666667x + x2 = 0 + -0.5238095238 Combine like terms: 0.5238095238 + -0.5238095238 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + -0.5238095238 -1.666666667x + x2 = 0 + -0.5238095238 Combine like terms: 0 + -0.5238095238 = -0.5238095238 -1.666666667x + x2 = -0.5238095238 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 = -0.5238095238 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.5238095238 + 0.6944444447 Combine like terms: -0.5238095238 + 0.6944444447 = 0.1706349209 0.6944444447 + -1.666666667x + x2 = 0.1706349209 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.1706349209 Calculate the square root of the right side: 0.4130798 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.4130798 and -0.4130798.Subproblem 1
x + -0.8333333335 = 0.4130798 Simplifying x + -0.8333333335 = 0.4130798 Reorder the terms: -0.8333333335 + x = 0.4130798 Solving -0.8333333335 + x = 0.4130798 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 = 0.4130798 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.4130798 + 0.8333333335 x = 0.4130798 + 0.8333333335 Combine like terms: 0.4130798 + 0.8333333335 = 1.2464131335 x = 1.2464131335 Simplifying x = 1.2464131335Subproblem 2
x + -0.8333333335 = -0.4130798 Simplifying x + -0.8333333335 = -0.4130798 Reorder the terms: -0.8333333335 + x = -0.4130798 Solving -0.8333333335 + x = -0.4130798 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 = -0.4130798 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.4130798 + 0.8333333335 x = -0.4130798 + 0.8333333335 Combine like terms: -0.4130798 + 0.8333333335 = 0.4202535335 x = 0.4202535335 Simplifying x = 0.4202535335Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2464131335, 0.4202535335}
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