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Simplifying (0.01x2) + 0.6x + 6.3 = 0 Reorder the terms: 6.3 + 0.6x + (0.01x2) = 0 Solving 6.3 + 0.6x + (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'. 630 + 60x + x2 = 0 Move the constant term to the right: Add '-630' to each side of the equation. 630 + 60x + -630 + x2 = 0 + -630 Reorder the terms: 630 + -630 + 60x + x2 = 0 + -630 Combine like terms: 630 + -630 = 0 0 + 60x + x2 = 0 + -630 60x + x2 = 0 + -630 Combine like terms: 0 + -630 = -630 60x + x2 = -630 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -630 + 900 Reorder the terms: 900 + 60x + x2 = -630 + 900 Combine like terms: -630 + 900 = 270 900 + 60x + x2 = 270 Factor a perfect square on the left side: ((x) + 30)((x) + 30) = 270 Calculate the square root of the right side: 16.431676725 Break this problem into two subproblems by setting ((x) + 30) equal to 16.431676725 and -16.431676725.Subproblem 1
(x) + 30 = 16.431676725 Simplifying (x) + 30 = 16.431676725 x + 30 = 16.431676725 Reorder the terms: 30 + x = 16.431676725 Solving 30 + x = 16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 16.431676725 + -30 Combine like terms: 30 + -30 = 0 0 + x = 16.431676725 + -30 x = 16.431676725 + -30 Combine like terms: 16.431676725 + -30 = -13.568323275 x = -13.568323275 Simplifying x = -13.568323275Subproblem 2
(x) + 30 = -16.431676725 Simplifying (x) + 30 = -16.431676725 x + 30 = -16.431676725 Reorder the terms: 30 + x = -16.431676725 Solving 30 + x = -16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -16.431676725 + -30 Combine like terms: 30 + -30 = 0 0 + x = -16.431676725 + -30 x = -16.431676725 + -30 Combine like terms: -16.431676725 + -30 = -46.431676725 x = -46.431676725 Simplifying x = -46.431676725Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.568323275, -46.431676725}
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