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Simplifying -8x(-3x + 6) = 4 + -1x Reorder the terms: -8x(6 + -3x) = 4 + -1x (6 * -8x + -3x * -8x) = 4 + -1x (-48x + 24x2) = 4 + -1x Solving -48x + 24x2 = 4 + -1x Solving for variable 'x'. Reorder the terms: -4 + -48x + x + 24x2 = 4 + -1x + -4 + x Combine like terms: -48x + x = -47x -4 + -47x + 24x2 = 4 + -1x + -4 + x Reorder the terms: -4 + -47x + 24x2 = 4 + -4 + -1x + x Combine like terms: 4 + -4 = 0 -4 + -47x + 24x2 = 0 + -1x + x -4 + -47x + 24x2 = -1x + x Combine like terms: -1x + x = 0 -4 + -47x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.1666666667 + -1.958333333x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.958333333x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.958333333x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.958333333x + x2 = 0 + 0.1666666667 -1.958333333x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.958333333x + x2 = 0.1666666667 The x term is -1.958333333x. Take half its coefficient (-0.9791666665). Square it (0.9587673608) and add it to both sides. Add '0.9587673608' to each side of the equation. -1.958333333x + 0.9587673608 + x2 = 0.1666666667 + 0.9587673608 Reorder the terms: 0.9587673608 + -1.958333333x + x2 = 0.1666666667 + 0.9587673608 Combine like terms: 0.1666666667 + 0.9587673608 = 1.1254340275 0.9587673608 + -1.958333333x + x2 = 1.1254340275 Factor a perfect square on the left side: (x + -0.9791666665)(x + -0.9791666665) = 1.1254340275 Calculate the square root of the right side: 1.060864755 Break this problem into two subproblems by setting (x + -0.9791666665) equal to 1.060864755 and -1.060864755.Subproblem 1
x + -0.9791666665 = 1.060864755 Simplifying x + -0.9791666665 = 1.060864755 Reorder the terms: -0.9791666665 + x = 1.060864755 Solving -0.9791666665 + x = 1.060864755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9791666665' to each side of the equation. -0.9791666665 + 0.9791666665 + x = 1.060864755 + 0.9791666665 Combine like terms: -0.9791666665 + 0.9791666665 = 0.0000000000 0.0000000000 + x = 1.060864755 + 0.9791666665 x = 1.060864755 + 0.9791666665 Combine like terms: 1.060864755 + 0.9791666665 = 2.0400314215 x = 2.0400314215 Simplifying x = 2.0400314215Subproblem 2
x + -0.9791666665 = -1.060864755 Simplifying x + -0.9791666665 = -1.060864755 Reorder the terms: -0.9791666665 + x = -1.060864755 Solving -0.9791666665 + x = -1.060864755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9791666665' to each side of the equation. -0.9791666665 + 0.9791666665 + x = -1.060864755 + 0.9791666665 Combine like terms: -0.9791666665 + 0.9791666665 = 0.0000000000 0.0000000000 + x = -1.060864755 + 0.9791666665 x = -1.060864755 + 0.9791666665 Combine like terms: -1.060864755 + 0.9791666665 = -0.0816980885 x = -0.0816980885 Simplifying x = -0.0816980885Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0400314215, -0.0816980885}
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