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Simplifying 7x2 + -14x + -13 = 0 Reorder the terms: -13 + -14x + 7x2 = 0 Solving -13 + -14x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -2x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -2x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -2x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.857142857 -2x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -2x + x2 = 1.857142857 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.857142857 + 1 Reorder the terms: 1 + -2x + x2 = 1.857142857 + 1 Combine like terms: 1.857142857 + 1 = 2.857142857 1 + -2x + x2 = 2.857142857 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.857142857 Calculate the square root of the right side: 1.690308509 Break this problem into two subproblems by setting (x + -1) equal to 1.690308509 and -1.690308509.Subproblem 1
x + -1 = 1.690308509 Simplifying x + -1 = 1.690308509 Reorder the terms: -1 + x = 1.690308509 Solving -1 + x = 1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.690308509 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.690308509 + 1 x = 1.690308509 + 1 Combine like terms: 1.690308509 + 1 = 2.690308509 x = 2.690308509 Simplifying x = 2.690308509Subproblem 2
x + -1 = -1.690308509 Simplifying x + -1 = -1.690308509 Reorder the terms: -1 + x = -1.690308509 Solving -1 + x = -1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.690308509 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.690308509 + 1 x = -1.690308509 + 1 Combine like terms: -1.690308509 + 1 = -0.690308509 x = -0.690308509 Simplifying x = -0.690308509Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.690308509, -0.690308509}
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