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Simplifying 0 = 0.6(x2) + 2.8x + 0.6 Reorder the terms: 0 = 0.6 + 2.8x + 0.6x2 Solving 0 = 0.6 + 2.8x + 0.6x2 Solving for variable 'x'. Combine like terms: 0 + -0.6 = -0.6 -0.6 + -2.8x + -0.6x2 = 0.6 + 2.8x + 0.6x2 + -0.6 + -2.8x + -0.6x2 Reorder the terms: -0.6 + -2.8x + -0.6x2 = 0.6 + -0.6 + 2.8x + -2.8x + 0.6x2 + -0.6x2 Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + -2.8x + -0.6x2 = 0.0 + 2.8x + -2.8x + 0.6x2 + -0.6x2 -0.6 + -2.8x + -0.6x2 = 2.8x + -2.8x + 0.6x2 + -0.6x2 Combine like terms: 2.8x + -2.8x = 0.0 -0.6 + -2.8x + -0.6x2 = 0.0 + 0.6x2 + -0.6x2 -0.6 + -2.8x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 -0.6 + -2.8x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 1 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.666666667x + x2 = 0 + -1 4.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.666666667x + x2 = -1 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -1 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -1 + 5.444444448 Combine like terms: -1 + 5.444444448 = 4.444444448 5.444444448 + 4.666666667x + x2 = 4.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 4.444444448 Calculate the square root of the right side: 2.108185108 Break this problem into two subproblems by setting (x + 2.333333334) equal to 2.108185108 and -2.108185108.Subproblem 1
x + 2.333333334 = 2.108185108 Simplifying x + 2.333333334 = 2.108185108 Reorder the terms: 2.333333334 + x = 2.108185108 Solving 2.333333334 + x = 2.108185108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 2.108185108 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.108185108 + -2.333333334 x = 2.108185108 + -2.333333334 Combine like terms: 2.108185108 + -2.333333334 = -0.225148226 x = -0.225148226 Simplifying x = -0.225148226Subproblem 2
x + 2.333333334 = -2.108185108 Simplifying x + 2.333333334 = -2.108185108 Reorder the terms: 2.333333334 + x = -2.108185108 Solving 2.333333334 + x = -2.108185108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -2.108185108 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.108185108 + -2.333333334 x = -2.108185108 + -2.333333334 Combine like terms: -2.108185108 + -2.333333334 = -4.441518442 x = -4.441518442 Simplifying x = -4.441518442Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.225148226, -4.441518442}
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