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Simplifying 4x2 + -23x + 8 = -2 + 3 Reorder the terms: 8 + -23x + 4x2 = -2 + 3 Combine like terms: -2 + 3 = 1 8 + -23x + 4x2 = 1 Solving 8 + -23x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: 8 + -1 + -23x + 4x2 = 1 + -1 Combine like terms: 8 + -1 = 7 7 + -23x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 7 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -5.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -5.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -5.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -5.75x + x2 = 0 + -1.75 -5.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -5.75x + x2 = -1.75 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 = -1.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -1.75 + 8.265625 Combine like terms: -1.75 + 8.265625 = 6.515625 8.265625 + -5.75x + x2 = 6.515625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (x + -2.875) equal to 2.552572232 and -2.552572232.Subproblem 1
x + -2.875 = 2.552572232 Simplifying x + -2.875 = 2.552572232 Reorder the terms: -2.875 + x = 2.552572232 Solving -2.875 + x = 2.552572232 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 = 2.552572232 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.552572232 + 2.875 x = 2.552572232 + 2.875 Combine like terms: 2.552572232 + 2.875 = 5.427572232 x = 5.427572232 Simplifying x = 5.427572232Subproblem 2
x + -2.875 = -2.552572232 Simplifying x + -2.875 = -2.552572232 Reorder the terms: -2.875 + x = -2.552572232 Solving -2.875 + x = -2.552572232 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 = -2.552572232 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.552572232 + 2.875 x = -2.552572232 + 2.875 Combine like terms: -2.552572232 + 2.875 = 0.322427768 x = 0.322427768 Simplifying x = 0.322427768Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.427572232, 0.322427768}
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