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Simplifying 0.36x2 = -0.84x + -0.49 Reorder the terms: 0.36x2 = -0.49 + -0.84x Solving 0.36x2 = -0.49 + -0.84x Solving for variable 'x'. Reorder the terms: 0.49 + 0.84x + 0.36x2 = -0.49 + -0.84x + 0.49 + 0.84x Reorder the terms: 0.49 + 0.84x + 0.36x2 = -0.49 + 0.49 + -0.84x + 0.84x Combine like terms: -0.49 + 0.49 = 0.00 0.49 + 0.84x + 0.36x2 = 0.00 + -0.84x + 0.84x 0.49 + 0.84x + 0.36x2 = -0.84x + 0.84x Combine like terms: -0.84x + 0.84x = 0.00 0.49 + 0.84x + 0.36x2 = 0.00 Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. 1.361111111 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-1.361111111' to each side of the equation. 1.361111111 + 2.333333333x + -1.361111111 + x2 = 0 + -1.361111111 Reorder the terms: 1.361111111 + -1.361111111 + 2.333333333x + x2 = 0 + -1.361111111 Combine like terms: 1.361111111 + -1.361111111 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + -1.361111111 2.333333333x + x2 = 0 + -1.361111111 Combine like terms: 0 + -1.361111111 = -1.361111111 2.333333333x + x2 = -1.361111111 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -1.361111111 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -1.361111111 + 1.361111112 Combine like terms: -1.361111111 + 1.361111112 = 0.000000001 1.361111112 + 2.333333333x + x2 = 0.000000001 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 0.000000001 Calculate the square root of the right side: 0.000031623 Break this problem into two subproblems by setting (x + 1.166666667) equal to 0.000031623 and -0.000031623.Subproblem 1
x + 1.166666667 = 0.000031623 Simplifying x + 1.166666667 = 0.000031623 Reorder the terms: 1.166666667 + x = 0.000031623 Solving 1.166666667 + x = 0.000031623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.000031623 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.000031623 + -1.166666667 x = 0.000031623 + -1.166666667 Combine like terms: 0.000031623 + -1.166666667 = -1.166635044 x = -1.166635044 Simplifying x = -1.166635044Subproblem 2
x + 1.166666667 = -0.000031623 Simplifying x + 1.166666667 = -0.000031623 Reorder the terms: 1.166666667 + x = -0.000031623 Solving 1.166666667 + x = -0.000031623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.000031623 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.000031623 + -1.166666667 x = -0.000031623 + -1.166666667 Combine like terms: -0.000031623 + -1.166666667 = -1.16669829 x = -1.16669829 Simplifying x = -1.16669829Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.166635044, -1.16669829}
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