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Simplifying -0.01x2 + 0.8x + 5.9 = 0 Reorder the terms: 5.9 + 0.8x + -0.01x2 = 0 Solving 5.9 + 0.8x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -590 + -80x + x2 = 0 Move the constant term to the right: Add '590' to each side of the equation. -590 + -80x + 590 + x2 = 0 + 590 Reorder the terms: -590 + 590 + -80x + x2 = 0 + 590 Combine like terms: -590 + 590 = 0 0 + -80x + x2 = 0 + 590 -80x + x2 = 0 + 590 Combine like terms: 0 + 590 = 590 -80x + x2 = 590 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 590 + 1600 Reorder the terms: 1600 + -80x + x2 = 590 + 1600 Combine like terms: 590 + 1600 = 2190 1600 + -80x + x2 = 2190 Factor a perfect square on the left side: (x + -40)(x + -40) = 2190 Calculate the square root of the right side: 46.797435827 Break this problem into two subproblems by setting (x + -40) equal to 46.797435827 and -46.797435827.Subproblem 1
x + -40 = 46.797435827 Simplifying x + -40 = 46.797435827 Reorder the terms: -40 + x = 46.797435827 Solving -40 + x = 46.797435827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 46.797435827 + 40 Combine like terms: -40 + 40 = 0 0 + x = 46.797435827 + 40 x = 46.797435827 + 40 Combine like terms: 46.797435827 + 40 = 86.797435827 x = 86.797435827 Simplifying x = 86.797435827Subproblem 2
x + -40 = -46.797435827 Simplifying x + -40 = -46.797435827 Reorder the terms: -40 + x = -46.797435827 Solving -40 + x = -46.797435827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -46.797435827 + 40 Combine like terms: -40 + 40 = 0 0 + x = -46.797435827 + 40 x = -46.797435827 + 40 Combine like terms: -46.797435827 + 40 = -6.797435827 x = -6.797435827 Simplifying x = -6.797435827Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.797435827, -6.797435827}
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