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Simplifying 102x2 + -6x + -106 = 0 Reorder the terms: -106 + -6x + 102x2 = 0 Solving -106 + -6x + 102x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-53 + -3x + 51x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-53 + -3x + 51x2)' equal to zero and attempt to solve: Simplifying -53 + -3x + 51x2 = 0 Solving -53 + -3x + 51x2 = 0 Begin completing the square. Divide all terms by 51 the coefficient of the squared term: Divide each side by '51'. -1.039215686 + -0.05882352941x + x2 = 0 Move the constant term to the right: Add '1.039215686' to each side of the equation. -1.039215686 + -0.05882352941x + 1.039215686 + x2 = 0 + 1.039215686 Reorder the terms: -1.039215686 + 1.039215686 + -0.05882352941x + x2 = 0 + 1.039215686 Combine like terms: -1.039215686 + 1.039215686 = 0.000000000 0.000000000 + -0.05882352941x + x2 = 0 + 1.039215686 -0.05882352941x + x2 = 0 + 1.039215686 Combine like terms: 0 + 1.039215686 = 1.039215686 -0.05882352941x + x2 = 1.039215686 The x term is -0.05882352941x. Take half its coefficient (-0.02941176471). Square it (0.0008650519034) and add it to both sides. Add '0.0008650519034' to each side of the equation. -0.05882352941x + 0.0008650519034 + x2 = 1.039215686 + 0.0008650519034 Reorder the terms: 0.0008650519034 + -0.05882352941x + x2 = 1.039215686 + 0.0008650519034 Combine like terms: 1.039215686 + 0.0008650519034 = 1.0400807379034 0.0008650519034 + -0.05882352941x + x2 = 1.0400807379034 Factor a perfect square on the left side: (x + -0.02941176471)(x + -0.02941176471) = 1.0400807379034 Calculate the square root of the right side: 1.019843487 Break this problem into two subproblems by setting (x + -0.02941176471) equal to 1.019843487 and -1.019843487.Subproblem 1
x + -0.02941176471 = 1.019843487 Simplifying x + -0.02941176471 = 1.019843487 Reorder the terms: -0.02941176471 + x = 1.019843487 Solving -0.02941176471 + x = 1.019843487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02941176471' to each side of the equation. -0.02941176471 + 0.02941176471 + x = 1.019843487 + 0.02941176471 Combine like terms: -0.02941176471 + 0.02941176471 = 0.00000000000 0.00000000000 + x = 1.019843487 + 0.02941176471 x = 1.019843487 + 0.02941176471 Combine like terms: 1.019843487 + 0.02941176471 = 1.04925525171 x = 1.04925525171 Simplifying x = 1.04925525171Subproblem 2
x + -0.02941176471 = -1.019843487 Simplifying x + -0.02941176471 = -1.019843487 Reorder the terms: -0.02941176471 + x = -1.019843487 Solving -0.02941176471 + x = -1.019843487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02941176471' to each side of the equation. -0.02941176471 + 0.02941176471 + x = -1.019843487 + 0.02941176471 Combine like terms: -0.02941176471 + 0.02941176471 = 0.00000000000 0.00000000000 + x = -1.019843487 + 0.02941176471 x = -1.019843487 + 0.02941176471 Combine like terms: -1.019843487 + 0.02941176471 = -0.99043172229 x = -0.99043172229 Simplifying x = -0.99043172229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.04925525171, -0.99043172229}Solution
x = {1.04925525171, -0.99043172229}
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