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Simplifying 34x2 + 6x + -7 = 0 Reorder the terms: -7 + 6x + 34x2 = 0 Solving -7 + 6x + 34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.2058823529 + 0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.2058823529' to each side of the equation. -0.2058823529 + 0.1764705882x + 0.2058823529 + x2 = 0 + 0.2058823529 Reorder the terms: -0.2058823529 + 0.2058823529 + 0.1764705882x + x2 = 0 + 0.2058823529 Combine like terms: -0.2058823529 + 0.2058823529 = 0.0000000000 0.0000000000 + 0.1764705882x + x2 = 0 + 0.2058823529 0.1764705882x + x2 = 0 + 0.2058823529 Combine like terms: 0 + 0.2058823529 = 0.2058823529 0.1764705882x + x2 = 0.2058823529 The x term is 0.1764705882x. Take half its coefficient (0.0882352941). Square it (0.007785467125) and add it to both sides. Add '0.007785467125' to each side of the equation. 0.1764705882x + 0.007785467125 + x2 = 0.2058823529 + 0.007785467125 Reorder the terms: 0.007785467125 + 0.1764705882x + x2 = 0.2058823529 + 0.007785467125 Combine like terms: 0.2058823529 + 0.007785467125 = 0.213667820025 0.007785467125 + 0.1764705882x + x2 = 0.213667820025 Factor a perfect square on the left side: (x + 0.0882352941)(x + 0.0882352941) = 0.213667820025 Calculate the square root of the right side: 0.462242166 Break this problem into two subproblems by setting (x + 0.0882352941) equal to 0.462242166 and -0.462242166.Subproblem 1
x + 0.0882352941 = 0.462242166 Simplifying x + 0.0882352941 = 0.462242166 Reorder the terms: 0.0882352941 + x = 0.462242166 Solving 0.0882352941 + x = 0.462242166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = 0.462242166 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = 0.462242166 + -0.0882352941 x = 0.462242166 + -0.0882352941 Combine like terms: 0.462242166 + -0.0882352941 = 0.3740068719 x = 0.3740068719 Simplifying x = 0.3740068719Subproblem 2
x + 0.0882352941 = -0.462242166 Simplifying x + 0.0882352941 = -0.462242166 Reorder the terms: 0.0882352941 + x = -0.462242166 Solving 0.0882352941 + x = -0.462242166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = -0.462242166 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = -0.462242166 + -0.0882352941 x = -0.462242166 + -0.0882352941 Combine like terms: -0.462242166 + -0.0882352941 = -0.5504774601 x = -0.5504774601 Simplifying x = -0.5504774601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3740068719, -0.5504774601}
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