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Simplifying 13x2 + -3x + -10 = x Reorder the terms: -10 + -3x + 13x2 = x Solving -10 + -3x + 13x2 = x Solving for variable 'x'. Reorder the terms: -10 + -3x + -1x + 13x2 = x + -1x Combine like terms: -3x + -1x = -4x -10 + -4x + 13x2 = x + -1x Combine like terms: x + -1x = 0 -10 + -4x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.7692307692 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '0.7692307692' to each side of the equation. -0.7692307692 + -0.3076923077x + 0.7692307692 + x2 = 0 + 0.7692307692 Reorder the terms: -0.7692307692 + 0.7692307692 + -0.3076923077x + x2 = 0 + 0.7692307692 Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000 0.0000000000 + -0.3076923077x + x2 = 0 + 0.7692307692 -0.3076923077x + x2 = 0 + 0.7692307692 Combine like terms: 0 + 0.7692307692 = 0.7692307692 -0.3076923077x + x2 = 0.7692307692 The x term is -0.3076923077x. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077x + 0.02366863907 + x2 = 0.7692307692 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 0.7692307692 + 0.02366863907 Combine like terms: 0.7692307692 + 0.02366863907 = 0.79289940827 0.02366863907 + -0.3076923077x + x2 = 0.79289940827 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 0.79289940827 Calculate the square root of the right side: 0.890448993 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 0.890448993 and -0.890448993.Subproblem 1
x + -0.1538461539 = 0.890448993 Simplifying x + -0.1538461539 = 0.890448993 Reorder the terms: -0.1538461539 + x = 0.890448993 Solving -0.1538461539 + x = 0.890448993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 0.890448993 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 0.890448993 + 0.1538461539 x = 0.890448993 + 0.1538461539 Combine like terms: 0.890448993 + 0.1538461539 = 1.0442951469 x = 1.0442951469 Simplifying x = 1.0442951469Subproblem 2
x + -0.1538461539 = -0.890448993 Simplifying x + -0.1538461539 = -0.890448993 Reorder the terms: -0.1538461539 + x = -0.890448993 Solving -0.1538461539 + x = -0.890448993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -0.890448993 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -0.890448993 + 0.1538461539 x = -0.890448993 + 0.1538461539 Combine like terms: -0.890448993 + 0.1538461539 = -0.7366028391 x = -0.7366028391 Simplifying x = -0.7366028391Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0442951469, -0.7366028391}
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