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Simplifying 6x(2x + 3x) + -2(9x2 + -5x) + -485 = 0 Combine like terms: 2x + 3x = 5x 6x(5x) + -2(9x2 + -5x) + -485 = 0 Remove parenthesis around (5x) 6x * 5x + -2(9x2 + -5x) + -485 = 0 Reorder the terms for easier multiplication: 6 * 5x * x + -2(9x2 + -5x) + -485 = 0 Multiply 6 * 5 30x * x + -2(9x2 + -5x) + -485 = 0 Multiply x * x 30x2 + -2(9x2 + -5x) + -485 = 0 Reorder the terms: 30x2 + -2(-5x + 9x2) + -485 = 0 30x2 + (-5x * -2 + 9x2 * -2) + -485 = 0 30x2 + (10x + -18x2) + -485 = 0 Reorder the terms: -485 + 10x + 30x2 + -18x2 = 0 Combine like terms: 30x2 + -18x2 = 12x2 -485 + 10x + 12x2 = 0 Solving -485 + 10x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -40.41666667 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '40.41666667' to each side of the equation. -40.41666667 + 0.8333333333x + 40.41666667 + x2 = 0 + 40.41666667 Reorder the terms: -40.41666667 + 40.41666667 + 0.8333333333x + x2 = 0 + 40.41666667 Combine like terms: -40.41666667 + 40.41666667 = 0.00000000 0.00000000 + 0.8333333333x + x2 = 0 + 40.41666667 0.8333333333x + x2 = 0 + 40.41666667 Combine like terms: 0 + 40.41666667 = 40.41666667 0.8333333333x + x2 = 40.41666667 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 40.41666667 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 40.41666667 + 0.1736111111 Combine like terms: 40.41666667 + 0.1736111111 = 40.5902777811 0.1736111111 + 0.8333333333x + x2 = 40.5902777811 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 40.5902777811 Calculate the square root of the right side: 6.371049975 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 6.371049975 and -6.371049975.Subproblem 1
x + 0.4166666667 = 6.371049975 Simplifying x + 0.4166666667 = 6.371049975 Reorder the terms: 0.4166666667 + x = 6.371049975 Solving 0.4166666667 + x = 6.371049975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 6.371049975 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 6.371049975 + -0.4166666667 x = 6.371049975 + -0.4166666667 Combine like terms: 6.371049975 + -0.4166666667 = 5.9543833083 x = 5.9543833083 Simplifying x = 5.9543833083Subproblem 2
x + 0.4166666667 = -6.371049975 Simplifying x + 0.4166666667 = -6.371049975 Reorder the terms: 0.4166666667 + x = -6.371049975 Solving 0.4166666667 + x = -6.371049975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -6.371049975 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -6.371049975 + -0.4166666667 x = -6.371049975 + -0.4166666667 Combine like terms: -6.371049975 + -0.4166666667 = -6.7877166417 x = -6.7877166417 Simplifying x = -6.7877166417Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9543833083, -6.7877166417}
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