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Simplifying 7x2 + 12x + -12 = 0 Reorder the terms: -12 + 12x + 7x2 = 0 Solving -12 + 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'. -1.714285714 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + 1.714285714x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + 1.714285714x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + 1.714285714x + x2 = 0 + 1.714285714 1.714285714x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 1.714285714x + x2 = 1.714285714 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 = 1.714285714 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 1.714285714 + 0.7346938773 Combine like terms: 1.714285714 + 0.7346938773 = 2.4489795913 0.7346938773 + 1.714285714x + x2 = 2.4489795913 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 2.4489795913 Calculate the square root of the right side: 1.564921593 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.564921593 and -1.564921593.Subproblem 1
x + 0.857142857 = 1.564921593 Simplifying x + 0.857142857 = 1.564921593 Reorder the terms: 0.857142857 + x = 1.564921593 Solving 0.857142857 + x = 1.564921593 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 = 1.564921593 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.564921593 + -0.857142857 x = 1.564921593 + -0.857142857 Combine like terms: 1.564921593 + -0.857142857 = 0.707778736 x = 0.707778736 Simplifying x = 0.707778736Subproblem 2
x + 0.857142857 = -1.564921593 Simplifying x + 0.857142857 = -1.564921593 Reorder the terms: 0.857142857 + x = -1.564921593 Solving 0.857142857 + x = -1.564921593 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 = -1.564921593 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.564921593 + -0.857142857 x = -1.564921593 + -0.857142857 Combine like terms: -1.564921593 + -0.857142857 = -2.42206445 x = -2.42206445 Simplifying x = -2.42206445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.707778736, -2.42206445}
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