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Simplifying 6x2 + 7x + -90 = 5 Reorder the terms: -90 + 7x + 6x2 = 5 Solving -90 + 7x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -90 + -5 + 7x + 6x2 = 5 + -5 Combine like terms: -90 + -5 = -95 -95 + 7x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -95 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -15.83333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '15.83333333' to each side of the equation. -15.83333333 + 1.166666667x + 15.83333333 + x2 = 0 + 15.83333333 Reorder the terms: -15.83333333 + 15.83333333 + 1.166666667x + x2 = 0 + 15.83333333 Combine like terms: -15.83333333 + 15.83333333 = 0.00000000 0.00000000 + 1.166666667x + x2 = 0 + 15.83333333 1.166666667x + x2 = 0 + 15.83333333 Combine like terms: 0 + 15.83333333 = 15.83333333 1.166666667x + x2 = 15.83333333 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 15.83333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 15.83333333 + 0.3402777780 Combine like terms: 15.83333333 + 0.3402777780 = 16.173611108 0.3402777780 + 1.166666667x + x2 = 16.173611108 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 16.173611108 Calculate the square root of the right side: 4.021642837 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 4.021642837 and -4.021642837.Subproblem 1
x + 0.5833333335 = 4.021642837 Simplifying x + 0.5833333335 = 4.021642837 Reorder the terms: 0.5833333335 + x = 4.021642837 Solving 0.5833333335 + x = 4.021642837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 4.021642837 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 4.021642837 + -0.5833333335 x = 4.021642837 + -0.5833333335 Combine like terms: 4.021642837 + -0.5833333335 = 3.4383095035 x = 3.4383095035 Simplifying x = 3.4383095035Subproblem 2
x + 0.5833333335 = -4.021642837 Simplifying x + 0.5833333335 = -4.021642837 Reorder the terms: 0.5833333335 + x = -4.021642837 Solving 0.5833333335 + x = -4.021642837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -4.021642837 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -4.021642837 + -0.5833333335 x = -4.021642837 + -0.5833333335 Combine like terms: -4.021642837 + -0.5833333335 = -4.6049761705 x = -4.6049761705 Simplifying x = -4.6049761705Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4383095035, -4.6049761705}
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