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Simplifying 4x2 + 15x + -23 = 0 Reorder the terms: -23 + 15x + 4x2 = 0 Solving -23 + 15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + 3.75x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 3.75x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 3.75x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 3.75x + x2 = 0 + 5.75 3.75x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 3.75x + x2 = 5.75 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 5.75 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 5.75 + 3.515625 Combine like terms: 5.75 + 3.515625 = 9.265625 3.515625 + 3.75x + x2 = 9.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 9.265625 Calculate the square root of the right side: 3.043948915 Break this problem into two subproblems by setting (x + 1.875) equal to 3.043948915 and -3.043948915.Subproblem 1
x + 1.875 = 3.043948915 Simplifying x + 1.875 = 3.043948915 Reorder the terms: 1.875 + x = 3.043948915 Solving 1.875 + x = 3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 3.043948915 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 3.043948915 + -1.875 x = 3.043948915 + -1.875 Combine like terms: 3.043948915 + -1.875 = 1.168948915 x = 1.168948915 Simplifying x = 1.168948915Subproblem 2
x + 1.875 = -3.043948915 Simplifying x + 1.875 = -3.043948915 Reorder the terms: 1.875 + x = -3.043948915 Solving 1.875 + x = -3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -3.043948915 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -3.043948915 + -1.875 x = -3.043948915 + -1.875 Combine like terms: -3.043948915 + -1.875 = -4.918948915 x = -4.918948915 Simplifying x = -4.918948915Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.168948915, -4.918948915}
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