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Simplifying 4x2 = 23x + 42 Reorder the terms: 4x2 = 42 + 23x Solving 4x2 = 42 + 23x Solving for variable 'x'. Reorder the terms: -42 + -23x + 4x2 = 42 + 23x + -42 + -23x Reorder the terms: -42 + -23x + 4x2 = 42 + -42 + 23x + -23x Combine like terms: 42 + -42 = 0 -42 + -23x + 4x2 = 0 + 23x + -23x -42 + -23x + 4x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -42 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.5 + -5.75x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -5.75x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -5.75x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -5.75x + x2 = 0 + 10.5 -5.75x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -5.75x + x2 = 10.5 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 10.5 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 10.5 + 8.265625 Combine like terms: 10.5 + 8.265625 = 18.765625 8.265625 + -5.75x + x2 = 18.765625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 18.765625 Calculate the square root of the right side: 4.331930863 Break this problem into two subproblems by setting (x + -2.875) equal to 4.331930863 and -4.331930863.Subproblem 1
x + -2.875 = 4.331930863 Simplifying x + -2.875 = 4.331930863 Reorder the terms: -2.875 + x = 4.331930863 Solving -2.875 + x = 4.331930863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 4.331930863 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 4.331930863 + 2.875 x = 4.331930863 + 2.875 Combine like terms: 4.331930863 + 2.875 = 7.206930863 x = 7.206930863 Simplifying x = 7.206930863Subproblem 2
x + -2.875 = -4.331930863 Simplifying x + -2.875 = -4.331930863 Reorder the terms: -2.875 + x = -4.331930863 Solving -2.875 + x = -4.331930863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -4.331930863 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -4.331930863 + 2.875 x = -4.331930863 + 2.875 Combine like terms: -4.331930863 + 2.875 = -1.456930863 x = -1.456930863 Simplifying x = -1.456930863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.206930863, -1.456930863}
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