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Simplifying -0.01x2 + 0.8x + 6.2 = 0 Reorder the terms: 6.2 + 0.8x + -0.01x2 = 0 Solving 6.2 + 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'. -620 + -80x + x2 = 0 Move the constant term to the right: Add '620' to each side of the equation. -620 + -80x + 620 + x2 = 0 + 620 Reorder the terms: -620 + 620 + -80x + x2 = 0 + 620 Combine like terms: -620 + 620 = 0 0 + -80x + x2 = 0 + 620 -80x + x2 = 0 + 620 Combine like terms: 0 + 620 = 620 -80x + x2 = 620 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 = 620 + 1600 Reorder the terms: 1600 + -80x + x2 = 620 + 1600 Combine like terms: 620 + 1600 = 2220 1600 + -80x + x2 = 2220 Factor a perfect square on the left side: (x + -40)(x + -40) = 2220 Calculate the square root of the right side: 47.116875958 Break this problem into two subproblems by setting (x + -40) equal to 47.116875958 and -47.116875958.Subproblem 1
x + -40 = 47.116875958 Simplifying x + -40 = 47.116875958 Reorder the terms: -40 + x = 47.116875958 Solving -40 + x = 47.116875958 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 = 47.116875958 + 40 Combine like terms: -40 + 40 = 0 0 + x = 47.116875958 + 40 x = 47.116875958 + 40 Combine like terms: 47.116875958 + 40 = 87.116875958 x = 87.116875958 Simplifying x = 87.116875958Subproblem 2
x + -40 = -47.116875958 Simplifying x + -40 = -47.116875958 Reorder the terms: -40 + x = -47.116875958 Solving -40 + x = -47.116875958 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 = -47.116875958 + 40 Combine like terms: -40 + 40 = 0 0 + x = -47.116875958 + 40 x = -47.116875958 + 40 Combine like terms: -47.116875958 + 40 = -7.116875958 x = -7.116875958 Simplifying x = -7.116875958Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.116875958, -7.116875958}
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