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Simplifying 4x2 + -23x + 54 = 6x + 4 Reorder the terms: 54 + -23x + 4x2 = 6x + 4 Reorder the terms: 54 + -23x + 4x2 = 4 + 6x Solving 54 + -23x + 4x2 = 4 + 6x Solving for variable 'x'. Reorder the terms: 54 + -4 + -23x + -6x + 4x2 = 4 + 6x + -4 + -6x Combine like terms: 54 + -4 = 50 50 + -23x + -6x + 4x2 = 4 + 6x + -4 + -6x Combine like terms: -23x + -6x = -29x 50 + -29x + 4x2 = 4 + 6x + -4 + -6x Reorder the terms: 50 + -29x + 4x2 = 4 + -4 + 6x + -6x Combine like terms: 4 + -4 = 0 50 + -29x + 4x2 = 0 + 6x + -6x 50 + -29x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 50 + -29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.5 + -7.25x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -7.25x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -7.25x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -7.25x + x2 = 0 + -12.5 -7.25x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -7.25x + x2 = -12.5 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -12.5 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -12.5 + 13.140625 Combine like terms: -12.5 + 13.140625 = 0.640625 13.140625 + -7.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + -3.625) equal to 0.80039053 and -0.80039053.Subproblem 1
x + -3.625 = 0.80039053 Simplifying x + -3.625 = 0.80039053 Reorder the terms: -3.625 + x = 0.80039053 Solving -3.625 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 0.80039053 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 0.80039053 + 3.625 x = 0.80039053 + 3.625 Combine like terms: 0.80039053 + 3.625 = 4.42539053 x = 4.42539053 Simplifying x = 4.42539053Subproblem 2
x + -3.625 = -0.80039053 Simplifying x + -3.625 = -0.80039053 Reorder the terms: -3.625 + x = -0.80039053 Solving -3.625 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -0.80039053 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -0.80039053 + 3.625 x = -0.80039053 + 3.625 Combine like terms: -0.80039053 + 3.625 = 2.82460947 x = 2.82460947 Simplifying x = 2.82460947Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.42539053, 2.82460947}
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