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Simplifying 5x2 + -13x + -160 = 0 Reorder the terms: -160 + -13x + 5x2 = 0 Solving -160 + -13x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -32 + -2.6x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -2.6x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -2.6x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -2.6x + x2 = 0 + 32 -2.6x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -2.6x + x2 = 32 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 32 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 32 + 1.69 Combine like terms: 32 + 1.69 = 33.69 1.69 + -2.6x + x2 = 33.69 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 33.69 Calculate the square root of the right side: 5.804308744 Break this problem into two subproblems by setting (x + -1.3) equal to 5.804308744 and -5.804308744.Subproblem 1
x + -1.3 = 5.804308744 Simplifying x + -1.3 = 5.804308744 Reorder the terms: -1.3 + x = 5.804308744 Solving -1.3 + x = 5.804308744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 5.804308744 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 5.804308744 + 1.3 x = 5.804308744 + 1.3 Combine like terms: 5.804308744 + 1.3 = 7.104308744 x = 7.104308744 Simplifying x = 7.104308744Subproblem 2
x + -1.3 = -5.804308744 Simplifying x + -1.3 = -5.804308744 Reorder the terms: -1.3 + x = -5.804308744 Solving -1.3 + x = -5.804308744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -5.804308744 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -5.804308744 + 1.3 x = -5.804308744 + 1.3 Combine like terms: -5.804308744 + 1.3 = -4.504308744 x = -4.504308744 Simplifying x = -4.504308744Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.104308744, -4.504308744}
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