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Simplifying -0.01x2 + 0.8x + 5.4 = 0 Reorder the terms: 5.4 + 0.8x + -0.01x2 = 0 Solving 5.4 + 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'. -540 + -80x + x2 = 0 Move the constant term to the right: Add '540' to each side of the equation. -540 + -80x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -80x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -80x + x2 = 0 + 540 -80x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -80x + x2 = 540 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 = 540 + 1600 Reorder the terms: 1600 + -80x + x2 = 540 + 1600 Combine like terms: 540 + 1600 = 2140 1600 + -80x + x2 = 2140 Factor a perfect square on the left side: (x + -40)(x + -40) = 2140 Calculate the square root of the right side: 46.260134025 Break this problem into two subproblems by setting (x + -40) equal to 46.260134025 and -46.260134025.Subproblem 1
x + -40 = 46.260134025 Simplifying x + -40 = 46.260134025 Reorder the terms: -40 + x = 46.260134025 Solving -40 + x = 46.260134025 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 = 46.260134025 + 40 Combine like terms: -40 + 40 = 0 0 + x = 46.260134025 + 40 x = 46.260134025 + 40 Combine like terms: 46.260134025 + 40 = 86.260134025 x = 86.260134025 Simplifying x = 86.260134025Subproblem 2
x + -40 = -46.260134025 Simplifying x + -40 = -46.260134025 Reorder the terms: -40 + x = -46.260134025 Solving -40 + x = -46.260134025 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 = -46.260134025 + 40 Combine like terms: -40 + 40 = 0 0 + x = -46.260134025 + 40 x = -46.260134025 + 40 Combine like terms: -46.260134025 + 40 = -6.260134025 x = -6.260134025 Simplifying x = -6.260134025Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.260134025, -6.260134025}
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