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Simplifying 15x2 + -2x + -6 = 0 Reorder the terms: -6 + -2x + 15x2 = 0 Solving -6 + -2x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + -0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.1333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.1333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.1333333333x + x2 = 0 + 0.4 -0.1333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.1333333333x + x2 = 0.4 The x term is -0.1333333333x. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333x + 0.004444444442 + x2 = 0.4 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333x + x2 = 0.4 + 0.004444444442 Combine like terms: 0.4 + 0.004444444442 = 0.404444444442 0.004444444442 + -0.1333333333x + x2 = 0.404444444442 Factor a perfect square on the left side: (x + -0.06666666665)(x + -0.06666666665) = 0.404444444442 Calculate the square root of the right side: 0.635959468 Break this problem into two subproblems by setting (x + -0.06666666665) equal to 0.635959468 and -0.635959468.Subproblem 1
x + -0.06666666665 = 0.635959468 Simplifying x + -0.06666666665 = 0.635959468 Reorder the terms: -0.06666666665 + x = 0.635959468 Solving -0.06666666665 + x = 0.635959468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = 0.635959468 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = 0.635959468 + 0.06666666665 x = 0.635959468 + 0.06666666665 Combine like terms: 0.635959468 + 0.06666666665 = 0.70262613465 x = 0.70262613465 Simplifying x = 0.70262613465Subproblem 2
x + -0.06666666665 = -0.635959468 Simplifying x + -0.06666666665 = -0.635959468 Reorder the terms: -0.06666666665 + x = -0.635959468 Solving -0.06666666665 + x = -0.635959468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = -0.635959468 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = -0.635959468 + 0.06666666665 x = -0.635959468 + 0.06666666665 Combine like terms: -0.635959468 + 0.06666666665 = -0.56929280135 x = -0.56929280135 Simplifying x = -0.56929280135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.70262613465, -0.56929280135}
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