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Simplifying 56x2 + -86x + -12 = 0 Reorder the terms: -12 + -86x + 56x2 = 0 Solving -12 + -86x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -43x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -43x + 28x2)' equal to zero and attempt to solve: Simplifying -6 + -43x + 28x2 = 0 Solving -6 + -43x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.2142857143 + -1.535714286x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -1.535714286x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -1.535714286x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -1.535714286x + x2 = 0 + 0.2142857143 -1.535714286x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -1.535714286x + x2 = 0.2142857143 The x term is -1.535714286x. Take half its coefficient (-0.767857143). Square it (0.5896045921) and add it to both sides. Add '0.5896045921' to each side of the equation. -1.535714286x + 0.5896045921 + x2 = 0.2142857143 + 0.5896045921 Reorder the terms: 0.5896045921 + -1.535714286x + x2 = 0.2142857143 + 0.5896045921 Combine like terms: 0.2142857143 + 0.5896045921 = 0.8038903064 0.5896045921 + -1.535714286x + x2 = 0.8038903064 Factor a perfect square on the left side: (x + -0.767857143)(x + -0.767857143) = 0.8038903064 Calculate the square root of the right side: 0.896599301 Break this problem into two subproblems by setting (x + -0.767857143) equal to 0.896599301 and -0.896599301.Subproblem 1
x + -0.767857143 = 0.896599301 Simplifying x + -0.767857143 = 0.896599301 Reorder the terms: -0.767857143 + x = 0.896599301 Solving -0.767857143 + x = 0.896599301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.767857143' to each side of the equation. -0.767857143 + 0.767857143 + x = 0.896599301 + 0.767857143 Combine like terms: -0.767857143 + 0.767857143 = 0.000000000 0.000000000 + x = 0.896599301 + 0.767857143 x = 0.896599301 + 0.767857143 Combine like terms: 0.896599301 + 0.767857143 = 1.664456444 x = 1.664456444 Simplifying x = 1.664456444Subproblem 2
x + -0.767857143 = -0.896599301 Simplifying x + -0.767857143 = -0.896599301 Reorder the terms: -0.767857143 + x = -0.896599301 Solving -0.767857143 + x = -0.896599301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.767857143' to each side of the equation. -0.767857143 + 0.767857143 + x = -0.896599301 + 0.767857143 Combine like terms: -0.767857143 + 0.767857143 = 0.000000000 0.000000000 + x = -0.896599301 + 0.767857143 x = -0.896599301 + 0.767857143 Combine like terms: -0.896599301 + 0.767857143 = -0.128742158 x = -0.128742158 Simplifying x = -0.128742158Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.664456444, -0.128742158}Solution
x = {1.664456444, -0.128742158}
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