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Simplifying 7x2 + -12x + -14 = 0 Reorder the terms: -14 + -12x + 7x2 = 0 Solving -14 + -12x + 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'. -2 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.714285714x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.714285714x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.714285714x + x2 = 0 + 2 -1.714285714x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.714285714x + x2 = 2 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 2 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 2 + 0.7346938773 Combine like terms: 2 + 0.7346938773 = 2.7346938773 0.7346938773 + -1.714285714x + x2 = 2.7346938773 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 2.7346938773 Calculate the square root of the right side: 1.653690986 Break this problem into two subproblems by setting (x + -0.857142857) equal to 1.653690986 and -1.653690986.Subproblem 1
x + -0.857142857 = 1.653690986 Simplifying x + -0.857142857 = 1.653690986 Reorder the terms: -0.857142857 + x = 1.653690986 Solving -0.857142857 + x = 1.653690986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 1.653690986 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 1.653690986 + 0.857142857 x = 1.653690986 + 0.857142857 Combine like terms: 1.653690986 + 0.857142857 = 2.510833843 x = 2.510833843 Simplifying x = 2.510833843Subproblem 2
x + -0.857142857 = -1.653690986 Simplifying x + -0.857142857 = -1.653690986 Reorder the terms: -0.857142857 + x = -1.653690986 Solving -0.857142857 + x = -1.653690986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -1.653690986 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -1.653690986 + 0.857142857 x = -1.653690986 + 0.857142857 Combine like terms: -1.653690986 + 0.857142857 = -0.796548129 x = -0.796548129 Simplifying x = -0.796548129Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.510833843, -0.796548129}
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