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Simplifying 81x2 = -6x + 30 Reorder the terms: 81x2 = 30 + -6x Solving 81x2 = 30 + -6x Solving for variable 'x'. Reorder the terms: -30 + 6x + 81x2 = 30 + -6x + -30 + 6x Reorder the terms: -30 + 6x + 81x2 = 30 + -30 + -6x + 6x Combine like terms: 30 + -30 = 0 -30 + 6x + 81x2 = 0 + -6x + 6x -30 + 6x + 81x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -30 + 6x + 81x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 2x + 27x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 2x + 27x2)' equal to zero and attempt to solve: Simplifying -10 + 2x + 27x2 = 0 Solving -10 + 2x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.3703703704 + 0.07407407407x + x2 = 0 Move the constant term to the right: Add '0.3703703704' to each side of the equation. -0.3703703704 + 0.07407407407x + 0.3703703704 + x2 = 0 + 0.3703703704 Reorder the terms: -0.3703703704 + 0.3703703704 + 0.07407407407x + x2 = 0 + 0.3703703704 Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000 0.0000000000 + 0.07407407407x + x2 = 0 + 0.3703703704 0.07407407407x + x2 = 0 + 0.3703703704 Combine like terms: 0 + 0.3703703704 = 0.3703703704 0.07407407407x + x2 = 0.3703703704 The x term is 0.07407407407x. Take half its coefficient (0.03703703704). Square it (0.001371742113) and add it to both sides. Add '0.001371742113' to each side of the equation. 0.07407407407x + 0.001371742113 + x2 = 0.3703703704 + 0.001371742113 Reorder the terms: 0.001371742113 + 0.07407407407x + x2 = 0.3703703704 + 0.001371742113 Combine like terms: 0.3703703704 + 0.001371742113 = 0.371742112513 0.001371742113 + 0.07407407407x + x2 = 0.371742112513 Factor a perfect square on the left side: (x + 0.03703703704)(x + 0.03703703704) = 0.371742112513 Calculate the square root of the right side: 0.609706579 Break this problem into two subproblems by setting (x + 0.03703703704) equal to 0.609706579 and -0.609706579.Subproblem 1
x + 0.03703703704 = 0.609706579 Simplifying x + 0.03703703704 = 0.609706579 Reorder the terms: 0.03703703704 + x = 0.609706579 Solving 0.03703703704 + x = 0.609706579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + x = 0.609706579 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x = 0.609706579 + -0.03703703704 x = 0.609706579 + -0.03703703704 Combine like terms: 0.609706579 + -0.03703703704 = 0.57266954196 x = 0.57266954196 Simplifying x = 0.57266954196Subproblem 2
x + 0.03703703704 = -0.609706579 Simplifying x + 0.03703703704 = -0.609706579 Reorder the terms: 0.03703703704 + x = -0.609706579 Solving 0.03703703704 + x = -0.609706579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + x = -0.609706579 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x = -0.609706579 + -0.03703703704 x = -0.609706579 + -0.03703703704 Combine like terms: -0.609706579 + -0.03703703704 = -0.64674361604 x = -0.64674361604 Simplifying x = -0.64674361604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.57266954196, -0.64674361604}Solution
x = {0.57266954196, -0.64674361604}
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