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Simplifying -13x2 + 3x + -4x2 + 7 = 0 Reorder the terms: 7 + 3x + -13x2 + -4x2 = 0 Combine like terms: -13x2 + -4x2 = -17x2 7 + 3x + -17x2 = 0 Solving 7 + 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 + -0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.4117647059' to each side of the equation. -0.4117647059 + -0.1764705882x + 0.4117647059 + x2 = 0 + 0.4117647059 Reorder the terms: -0.4117647059 + 0.4117647059 + -0.1764705882x + x2 = 0 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + -0.1764705882x + x2 = 0 + 0.4117647059 -0.1764705882x + x2 = 0 + 0.4117647059 Combine like terms: 0 + 0.4117647059 = 0.4117647059 -0.1764705882x + x2 = 0.4117647059 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 = 0.4117647059 + 0.007785467125 Reorder the terms: 0.007785467125 + -0.1764705882x + x2 = 0.4117647059 + 0.007785467125 Combine like terms: 0.4117647059 + 0.007785467125 = 0.419550173025 0.007785467125 + -0.1764705882x + x2 = 0.419550173025 Factor a perfect square on the left side: (x + -0.0882352941)(x + -0.0882352941) = 0.419550173025 Calculate the square root of the right side: 0.647726928 Break this problem into two subproblems by setting (x + -0.0882352941) equal to 0.647726928 and -0.647726928.Subproblem 1
x + -0.0882352941 = 0.647726928 Simplifying x + -0.0882352941 = 0.647726928 Reorder the terms: -0.0882352941 + x = 0.647726928 Solving -0.0882352941 + x = 0.647726928 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 = 0.647726928 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = 0.647726928 + 0.0882352941 x = 0.647726928 + 0.0882352941 Combine like terms: 0.647726928 + 0.0882352941 = 0.7359622221 x = 0.7359622221 Simplifying x = 0.7359622221Subproblem 2
x + -0.0882352941 = -0.647726928 Simplifying x + -0.0882352941 = -0.647726928 Reorder the terms: -0.0882352941 + x = -0.647726928 Solving -0.0882352941 + x = -0.647726928 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 = -0.647726928 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = -0.647726928 + 0.0882352941 x = -0.647726928 + 0.0882352941 Combine like terms: -0.647726928 + 0.0882352941 = -0.5594916339 x = -0.5594916339 Simplifying x = -0.5594916339Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7359622221, -0.5594916339}
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