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Simplifying 13x2 + -14x = 1 Reorder the terms: -14x + 13x2 = 1 Solving -14x + 13x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -14x + 13x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -14x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.07692307692 + -1.076923077x + x2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + -1.076923077x + 0.07692307692 + x2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + -1.076923077x + x2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + -1.076923077x + x2 = 0 + 0.07692307692 -1.076923077x + x2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 -1.076923077x + x2 = 0.07692307692 The x term is -1.076923077x. Take half its coefficient (-0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. -1.076923077x + 0.2899408284 + x2 = 0.07692307692 + 0.2899408284 Reorder the terms: 0.2899408284 + -1.076923077x + x2 = 0.07692307692 + 0.2899408284 Combine like terms: 0.07692307692 + 0.2899408284 = 0.36686390532 0.2899408284 + -1.076923077x + x2 = 0.36686390532 Factor a perfect square on the left side: (x + -0.5384615385)(x + -0.5384615385) = 0.36686390532 Calculate the square root of the right side: 0.605692913 Break this problem into two subproblems by setting (x + -0.5384615385) equal to 0.605692913 and -0.605692913.Subproblem 1
x + -0.5384615385 = 0.605692913 Simplifying x + -0.5384615385 = 0.605692913 Reorder the terms: -0.5384615385 + x = 0.605692913 Solving -0.5384615385 + x = 0.605692913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = 0.605692913 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = 0.605692913 + 0.5384615385 x = 0.605692913 + 0.5384615385 Combine like terms: 0.605692913 + 0.5384615385 = 1.1441544515 x = 1.1441544515 Simplifying x = 1.1441544515Subproblem 2
x + -0.5384615385 = -0.605692913 Simplifying x + -0.5384615385 = -0.605692913 Reorder the terms: -0.5384615385 + x = -0.605692913 Solving -0.5384615385 + x = -0.605692913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = -0.605692913 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = -0.605692913 + 0.5384615385 x = -0.605692913 + 0.5384615385 Combine like terms: -0.605692913 + 0.5384615385 = -0.0672313745 x = -0.0672313745 Simplifying x = -0.0672313745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1441544515, -0.0672313745}
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