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Simplifying -0.22x2 + 30x + -210 = 0 Reorder the terms: -210 + 30x + -0.22x2 = 0 Solving -210 + 30x + -0.22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.22 the coefficient of the squared term: Divide each side by '-0.22'. 954.5454545 + -136.3636364x + x2 = 0 Move the constant term to the right: Add '-954.5454545' to each side of the equation. 954.5454545 + -136.3636364x + -954.5454545 + x2 = 0 + -954.5454545 Reorder the terms: 954.5454545 + -954.5454545 + -136.3636364x + x2 = 0 + -954.5454545 Combine like terms: 954.5454545 + -954.5454545 = 0.0000000 0.0000000 + -136.3636364x + x2 = 0 + -954.5454545 -136.3636364x + x2 = 0 + -954.5454545 Combine like terms: 0 + -954.5454545 = -954.5454545 -136.3636364x + x2 = -954.5454545 The x term is -136.3636364x. Take half its coefficient (-68.1818182). Square it (4648.760333) and add it to both sides. Add '4648.760333' to each side of the equation. -136.3636364x + 4648.760333 + x2 = -954.5454545 + 4648.760333 Reorder the terms: 4648.760333 + -136.3636364x + x2 = -954.5454545 + 4648.760333 Combine like terms: -954.5454545 + 4648.760333 = 3694.2148785 4648.760333 + -136.3636364x + x2 = 3694.2148785 Factor a perfect square on the left side: (x + -68.1818182)(x + -68.1818182) = 3694.2148785 Calculate the square root of the right side: 60.780053295 Break this problem into two subproblems by setting (x + -68.1818182) equal to 60.780053295 and -60.780053295.Subproblem 1
x + -68.1818182 = 60.780053295 Simplifying x + -68.1818182 = 60.780053295 Reorder the terms: -68.1818182 + x = 60.780053295 Solving -68.1818182 + x = 60.780053295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.1818182' to each side of the equation. -68.1818182 + 68.1818182 + x = 60.780053295 + 68.1818182 Combine like terms: -68.1818182 + 68.1818182 = 0.0000000 0.0000000 + x = 60.780053295 + 68.1818182 x = 60.780053295 + 68.1818182 Combine like terms: 60.780053295 + 68.1818182 = 128.961871495 x = 128.961871495 Simplifying x = 128.961871495Subproblem 2
x + -68.1818182 = -60.780053295 Simplifying x + -68.1818182 = -60.780053295 Reorder the terms: -68.1818182 + x = -60.780053295 Solving -68.1818182 + x = -60.780053295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.1818182' to each side of the equation. -68.1818182 + 68.1818182 + x = -60.780053295 + 68.1818182 Combine like terms: -68.1818182 + 68.1818182 = 0.0000000 0.0000000 + x = -60.780053295 + 68.1818182 x = -60.780053295 + 68.1818182 Combine like terms: -60.780053295 + 68.1818182 = 7.401764905 x = 7.401764905 Simplifying x = 7.401764905Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.961871495, 7.401764905}
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