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Simplifying 1720 = 5x2 + -4x Reorder the terms: 1720 = -4x + 5x2 Solving 1720 = -4x + 5x2 Solving for variable 'x'. Reorder the terms: 1720 + 4x + -5x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 1720 + 4x + -5x2 = 0 + 5x2 + -5x2 1720 + 4x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1720 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -344 + -0.8x + x2 = 0 Move the constant term to the right: Add '344' to each side of the equation. -344 + -0.8x + 344 + x2 = 0 + 344 Reorder the terms: -344 + 344 + -0.8x + x2 = 0 + 344 Combine like terms: -344 + 344 = 0 0 + -0.8x + x2 = 0 + 344 -0.8x + x2 = 0 + 344 Combine like terms: 0 + 344 = 344 -0.8x + x2 = 344 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 344 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 344 + 0.16 Combine like terms: 344 + 0.16 = 344.16 0.16 + -0.8x + x2 = 344.16 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 344.16 Calculate the square root of the right side: 18.5515498 Break this problem into two subproblems by setting (x + -0.4) equal to 18.5515498 and -18.5515498.Subproblem 1
x + -0.4 = 18.5515498 Simplifying x + -0.4 = 18.5515498 Reorder the terms: -0.4 + x = 18.5515498 Solving -0.4 + x = 18.5515498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 18.5515498 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 18.5515498 + 0.4 x = 18.5515498 + 0.4 Combine like terms: 18.5515498 + 0.4 = 18.9515498 x = 18.9515498 Simplifying x = 18.9515498Subproblem 2
x + -0.4 = -18.5515498 Simplifying x + -0.4 = -18.5515498 Reorder the terms: -0.4 + x = -18.5515498 Solving -0.4 + x = -18.5515498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -18.5515498 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -18.5515498 + 0.4 x = -18.5515498 + 0.4 Combine like terms: -18.5515498 + 0.4 = -18.1515498 x = -18.1515498 Simplifying x = -18.1515498Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.9515498, -18.1515498}
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