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Simplifying 5x2 + -59x + 160 = 0 Reorder the terms: 160 + -59x + 5x2 = 0 Solving 160 + -59x + 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 + -11.8x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -11.8x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -11.8x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -11.8x + x2 = 0 + -32 -11.8x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -11.8x + x2 = -32 The x term is -11.8x. Take half its coefficient (-5.9). Square it (34.81) and add it to both sides. Add '34.81' to each side of the equation. -11.8x + 34.81 + x2 = -32 + 34.81 Reorder the terms: 34.81 + -11.8x + x2 = -32 + 34.81 Combine like terms: -32 + 34.81 = 2.81 34.81 + -11.8x + x2 = 2.81 Factor a perfect square on the left side: (x + -5.9)(x + -5.9) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (x + -5.9) equal to 1.676305461 and -1.676305461.Subproblem 1
x + -5.9 = 1.676305461 Simplifying x + -5.9 = 1.676305461 Reorder the terms: -5.9 + x = 1.676305461 Solving -5.9 + x = 1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9' to each side of the equation. -5.9 + 5.9 + x = 1.676305461 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + x = 1.676305461 + 5.9 x = 1.676305461 + 5.9 Combine like terms: 1.676305461 + 5.9 = 7.576305461 x = 7.576305461 Simplifying x = 7.576305461Subproblem 2
x + -5.9 = -1.676305461 Simplifying x + -5.9 = -1.676305461 Reorder the terms: -5.9 + x = -1.676305461 Solving -5.9 + x = -1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9' to each side of the equation. -5.9 + 5.9 + x = -1.676305461 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + x = -1.676305461 + 5.9 x = -1.676305461 + 5.9 Combine like terms: -1.676305461 + 5.9 = 4.223694539 x = 4.223694539 Simplifying x = 4.223694539Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.576305461, 4.223694539}
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