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Simplifying 46x + -12 = 4x2 Reorder the terms: -12 + 46x = 4x2 Solving -12 + 46x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 -12 + 46x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 23x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 23x + -2x2)' equal to zero and attempt to solve: Simplifying -6 + 23x + -2x2 = 0 Solving -6 + 23x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3 + -11.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -11.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11.5x + x2 = 0 + -3 -11.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11.5x + x2 = -3 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -3 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -3 + 33.0625 Combine like terms: -3 + 33.0625 = 30.0625 33.0625 + -11.5x + x2 = 30.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (x + -5.75) equal to 5.48292805 and -5.48292805.Subproblem 1
x + -5.75 = 5.48292805 Simplifying x + -5.75 = 5.48292805 Reorder the terms: -5.75 + x = 5.48292805 Solving -5.75 + x = 5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 5.48292805 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 5.48292805 + 5.75 x = 5.48292805 + 5.75 Combine like terms: 5.48292805 + 5.75 = 11.23292805 x = 11.23292805 Simplifying x = 11.23292805Subproblem 2
x + -5.75 = -5.48292805 Simplifying x + -5.75 = -5.48292805 Reorder the terms: -5.75 + x = -5.48292805 Solving -5.75 + x = -5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -5.48292805 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -5.48292805 + 5.75 x = -5.48292805 + 5.75 Combine like terms: -5.48292805 + 5.75 = 0.26707195 x = 0.26707195 Simplifying x = 0.26707195Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.23292805, 0.26707195}Solution
x = {11.23292805, 0.26707195}
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