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Simplifying 0 = -6x2 + 4x + 3 Reorder the terms: 0 = 3 + 4x + -6x2 Solving 0 = 3 + 4x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -4x + 6x2 = 3 + 4x + -6x2 + -3 + -4x + 6x2 Reorder the terms: -3 + -4x + 6x2 = 3 + -3 + 4x + -4x + -6x2 + 6x2 Combine like terms: 3 + -3 = 0 -3 + -4x + 6x2 = 0 + 4x + -4x + -6x2 + 6x2 -3 + -4x + 6x2 = 4x + -4x + -6x2 + 6x2 Combine like terms: 4x + -4x = 0 -3 + -4x + 6x2 = 0 + -6x2 + 6x2 -3 + -4x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -3 + -4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.6666666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.6666666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 0.5 -0.6666666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.6666666667x + x2 = 0.5 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.5 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.5 + 0.1111111112 Combine like terms: 0.5 + 0.1111111112 = 0.6111111112 0.1111111112 + -0.6666666667x + x2 = 0.6111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.6111111112 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.78173596 and -0.78173596.Subproblem 1
x + -0.3333333334 = 0.78173596 Simplifying x + -0.3333333334 = 0.78173596 Reorder the terms: -0.3333333334 + x = 0.78173596 Solving -0.3333333334 + x = 0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.78173596 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.78173596 + 0.3333333334 x = 0.78173596 + 0.3333333334 Combine like terms: 0.78173596 + 0.3333333334 = 1.1150692934 x = 1.1150692934 Simplifying x = 1.1150692934Subproblem 2
x + -0.3333333334 = -0.78173596 Simplifying x + -0.3333333334 = -0.78173596 Reorder the terms: -0.3333333334 + x = -0.78173596 Solving -0.3333333334 + x = -0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.78173596 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.78173596 + 0.3333333334 x = -0.78173596 + 0.3333333334 Combine like terms: -0.78173596 + 0.3333333334 = -0.4484026266 x = -0.4484026266 Simplifying x = -0.4484026266Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1150692934, -0.4484026266}
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