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Simplifying 3x2 + 29x + -12 = 0 Reorder the terms: -12 + 29x + 3x2 = 0 Solving -12 + 29x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 9.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 9.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 9.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 9.666666667x + x2 = 0 + 4 9.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 9.666666667x + x2 = 4 The x term is 9.666666667x. Take half its coefficient (4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. 9.666666667x + 23.36111112 + x2 = 4 + 23.36111112 Reorder the terms: 23.36111112 + 9.666666667x + x2 = 4 + 23.36111112 Combine like terms: 4 + 23.36111112 = 27.36111112 23.36111112 + 9.666666667x + x2 = 27.36111112 Factor a perfect square on the left side: (x + 4.833333334)(x + 4.833333334) = 27.36111112 Calculate the square root of the right side: 5.230784943 Break this problem into two subproblems by setting (x + 4.833333334) equal to 5.230784943 and -5.230784943.Subproblem 1
x + 4.833333334 = 5.230784943 Simplifying x + 4.833333334 = 5.230784943 Reorder the terms: 4.833333334 + x = 5.230784943 Solving 4.833333334 + x = 5.230784943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + x = 5.230784943 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = 5.230784943 + -4.833333334 x = 5.230784943 + -4.833333334 Combine like terms: 5.230784943 + -4.833333334 = 0.397451609 x = 0.397451609 Simplifying x = 0.397451609Subproblem 2
x + 4.833333334 = -5.230784943 Simplifying x + 4.833333334 = -5.230784943 Reorder the terms: 4.833333334 + x = -5.230784943 Solving 4.833333334 + x = -5.230784943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + x = -5.230784943 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = -5.230784943 + -4.833333334 x = -5.230784943 + -4.833333334 Combine like terms: -5.230784943 + -4.833333334 = -10.064118277 x = -10.064118277 Simplifying x = -10.064118277Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.397451609, -10.064118277}
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