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Simplifying (-0.3x * -0.3x) + 6x + 12 = 0 Reorder the terms for easier multiplication: (-0.3 * -0.3x * x) + 6x + 12 = 0 Multiply -0.3 * -0.3 (0.09x * x) + 6x + 12 = 0 Multiply x * x (0.09x2) + 6x + 12 = 0 Reorder the terms: 12 + 6x + (0.09x2) = 0 Solving 12 + 6x + (0.09x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. 133.3333333 + 66.66666667x + x2 = 0 Move the constant term to the right: Add '-133.3333333' to each side of the equation. 133.3333333 + 66.66666667x + -133.3333333 + x2 = 0 + -133.3333333 Reorder the terms: 133.3333333 + -133.3333333 + 66.66666667x + x2 = 0 + -133.3333333 Combine like terms: 133.3333333 + -133.3333333 = 0.0000000 0.0000000 + 66.66666667x + x2 = 0 + -133.3333333 66.66666667x + x2 = 0 + -133.3333333 Combine like terms: 0 + -133.3333333 = -133.3333333 66.66666667x + x2 = -133.3333333 The x term is 66.66666667x. Take half its coefficient (33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. 66.66666667x + 1111.111112 + x2 = -133.3333333 + 1111.111112 Reorder the terms: 1111.111112 + 66.66666667x + x2 = -133.3333333 + 1111.111112 Combine like terms: -133.3333333 + 1111.111112 = 977.7777787 1111.111112 + 66.66666667x + x2 = 977.7777787 Factor a perfect square on the left side: ((x) + 33.33333334)((x) + 33.33333334) = 977.7777787 Calculate the square root of the right side: 31.269438414 Break this problem into two subproblems by setting ((x) + 33.33333334) equal to 31.269438414 and -31.269438414.Subproblem 1
(x) + 33.33333334 = 31.269438414 Simplifying (x) + 33.33333334 = 31.269438414 x + 33.33333334 = 31.269438414 Reorder the terms: 33.33333334 + x = 31.269438414 Solving 33.33333334 + x = 31.269438414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = 31.269438414 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = 31.269438414 + -33.33333334 x = 31.269438414 + -33.33333334 Combine like terms: 31.269438414 + -33.33333334 = -2.063894926 x = -2.063894926 Simplifying x = -2.063894926Subproblem 2
(x) + 33.33333334 = -31.269438414 Simplifying (x) + 33.33333334 = -31.269438414 x + 33.33333334 = -31.269438414 Reorder the terms: 33.33333334 + x = -31.269438414 Solving 33.33333334 + x = -31.269438414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = -31.269438414 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = -31.269438414 + -33.33333334 x = -31.269438414 + -33.33333334 Combine like terms: -31.269438414 + -33.33333334 = -64.602771754 x = -64.602771754 Simplifying x = -64.602771754Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.063894926, -64.602771754}
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