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Simplifying 3X2 + 8X = -3 Reorder the terms: 8X + 3X2 = -3 Solving 8X + 3X2 = -3 Solving for variable 'X'. Reorder the terms: 3 + 8X + 3X2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 8X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 2.666666667X + X2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.666666667X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + 2.666666667X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.666666667X + X2 = 0 + -1 2.666666667X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.666666667X + X2 = -1 The X term is 2.666666667X. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667X + 1.777777780 + X2 = -1 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667X + X2 = -1 + 1.777777780 Combine like terms: -1 + 1.777777780 = 0.77777778 1.777777780 + 2.666666667X + X2 = 0.77777778 Factor a perfect square on the left side: (X + 1.333333334)(X + 1.333333334) = 0.77777778 Calculate the square root of the right side: 0.881917105 Break this problem into two subproblems by setting (X + 1.333333334) equal to 0.881917105 and -0.881917105.Subproblem 1
X + 1.333333334 = 0.881917105 Simplifying X + 1.333333334 = 0.881917105 Reorder the terms: 1.333333334 + X = 0.881917105 Solving 1.333333334 + X = 0.881917105 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + X = 0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + X = 0.881917105 + -1.333333334 X = 0.881917105 + -1.333333334 Combine like terms: 0.881917105 + -1.333333334 = -0.451416229 X = -0.451416229 Simplifying X = -0.451416229Subproblem 2
X + 1.333333334 = -0.881917105 Simplifying X + 1.333333334 = -0.881917105 Reorder the terms: 1.333333334 + X = -0.881917105 Solving 1.333333334 + X = -0.881917105 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + X = -0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + X = -0.881917105 + -1.333333334 X = -0.881917105 + -1.333333334 Combine like terms: -0.881917105 + -1.333333334 = -2.215250439 X = -2.215250439 Simplifying X = -2.215250439Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.451416229, -2.215250439}
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