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Simplifying 14x2 + 13x + -160 = 0 Reorder the terms: -160 + 13x + 14x2 = 0 Solving -160 + 13x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -11.42857143 + 0.9285714286x + x2 = 0 Move the constant term to the right: Add '11.42857143' to each side of the equation. -11.42857143 + 0.9285714286x + 11.42857143 + x2 = 0 + 11.42857143 Reorder the terms: -11.42857143 + 11.42857143 + 0.9285714286x + x2 = 0 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + 0.9285714286x + x2 = 0 + 11.42857143 0.9285714286x + x2 = 0 + 11.42857143 Combine like terms: 0 + 11.42857143 = 11.42857143 0.9285714286x + x2 = 11.42857143 The x term is 0.9285714286x. Take half its coefficient (0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. 0.9285714286x + 0.2155612245 + x2 = 11.42857143 + 0.2155612245 Reorder the terms: 0.2155612245 + 0.9285714286x + x2 = 11.42857143 + 0.2155612245 Combine like terms: 11.42857143 + 0.2155612245 = 11.6441326545 0.2155612245 + 0.9285714286x + x2 = 11.6441326545 Factor a perfect square on the left side: (x + 0.4642857143)(x + 0.4642857143) = 11.6441326545 Calculate the square root of the right side: 3.412350019 Break this problem into two subproblems by setting (x + 0.4642857143) equal to 3.412350019 and -3.412350019.Subproblem 1
x + 0.4642857143 = 3.412350019 Simplifying x + 0.4642857143 = 3.412350019 Reorder the terms: 0.4642857143 + x = 3.412350019 Solving 0.4642857143 + x = 3.412350019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = 3.412350019 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = 3.412350019 + -0.4642857143 x = 3.412350019 + -0.4642857143 Combine like terms: 3.412350019 + -0.4642857143 = 2.9480643047 x = 2.9480643047 Simplifying x = 2.9480643047Subproblem 2
x + 0.4642857143 = -3.412350019 Simplifying x + 0.4642857143 = -3.412350019 Reorder the terms: 0.4642857143 + x = -3.412350019 Solving 0.4642857143 + x = -3.412350019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = -3.412350019 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = -3.412350019 + -0.4642857143 x = -3.412350019 + -0.4642857143 Combine like terms: -3.412350019 + -0.4642857143 = -3.8766357333 x = -3.8766357333 Simplifying x = -3.8766357333Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9480643047, -3.8766357333}
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