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Simplifying 17x2 + 9.3x + -7 = 0 Reorder the terms: -7 + 9.3x + 17x2 = 0 Solving -7 + 9.3x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.4117647059 + 0.5470588235x + x2 = 0 Move the constant term to the right: Add '0.4117647059' to each side of the equation. -0.4117647059 + 0.5470588235x + 0.4117647059 + x2 = 0 + 0.4117647059 Reorder the terms: -0.4117647059 + 0.4117647059 + 0.5470588235x + x2 = 0 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + 0.5470588235x + x2 = 0 + 0.4117647059 0.5470588235x + x2 = 0 + 0.4117647059 Combine like terms: 0 + 0.4117647059 = 0.4117647059 0.5470588235x + x2 = 0.4117647059 The x term is 0.5470588235x. Take half its coefficient (0.2735294118). Square it (0.07481833912) and add it to both sides. Add '0.07481833912' to each side of the equation. 0.5470588235x + 0.07481833912 + x2 = 0.4117647059 + 0.07481833912 Reorder the terms: 0.07481833912 + 0.5470588235x + x2 = 0.4117647059 + 0.07481833912 Combine like terms: 0.4117647059 + 0.07481833912 = 0.48658304502 0.07481833912 + 0.5470588235x + x2 = 0.48658304502 Factor a perfect square on the left side: (x + 0.2735294118)(x + 0.2735294118) = 0.48658304502 Calculate the square root of the right side: 0.697555048 Break this problem into two subproblems by setting (x + 0.2735294118) equal to 0.697555048 and -0.697555048.Subproblem 1
x + 0.2735294118 = 0.697555048 Simplifying x + 0.2735294118 = 0.697555048 Reorder the terms: 0.2735294118 + x = 0.697555048 Solving 0.2735294118 + x = 0.697555048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2735294118' to each side of the equation. 0.2735294118 + -0.2735294118 + x = 0.697555048 + -0.2735294118 Combine like terms: 0.2735294118 + -0.2735294118 = 0.0000000000 0.0000000000 + x = 0.697555048 + -0.2735294118 x = 0.697555048 + -0.2735294118 Combine like terms: 0.697555048 + -0.2735294118 = 0.4240256362 x = 0.4240256362 Simplifying x = 0.4240256362Subproblem 2
x + 0.2735294118 = -0.697555048 Simplifying x + 0.2735294118 = -0.697555048 Reorder the terms: 0.2735294118 + x = -0.697555048 Solving 0.2735294118 + x = -0.697555048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2735294118' to each side of the equation. 0.2735294118 + -0.2735294118 + x = -0.697555048 + -0.2735294118 Combine like terms: 0.2735294118 + -0.2735294118 = 0.0000000000 0.0000000000 + x = -0.697555048 + -0.2735294118 x = -0.697555048 + -0.2735294118 Combine like terms: -0.697555048 + -0.2735294118 = -0.9710844598 x = -0.9710844598 Simplifying x = -0.9710844598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4240256362, -0.9710844598}
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