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Simplifying 4x2 + 23x = 28 Reorder the terms: 23x + 4x2 = 28 Solving 23x + 4x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 23x + 4x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + 5.75x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 5.75x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 5.75x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5.75x + x2 = 0 + 7 5.75x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 5.75x + x2 = 7 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 = 7 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 7 + 8.265625 Combine like terms: 7 + 8.265625 = 15.265625 8.265625 + 5.75x + x2 = 15.265625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 15.265625 Calculate the square root of the right side: 3.907124902 Break this problem into two subproblems by setting (x + 2.875) equal to 3.907124902 and -3.907124902.Subproblem 1
x + 2.875 = 3.907124902 Simplifying x + 2.875 = 3.907124902 Reorder the terms: 2.875 + x = 3.907124902 Solving 2.875 + x = 3.907124902 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 = 3.907124902 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 3.907124902 + -2.875 x = 3.907124902 + -2.875 Combine like terms: 3.907124902 + -2.875 = 1.032124902 x = 1.032124902 Simplifying x = 1.032124902Subproblem 2
x + 2.875 = -3.907124902 Simplifying x + 2.875 = -3.907124902 Reorder the terms: 2.875 + x = -3.907124902 Solving 2.875 + x = -3.907124902 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 = -3.907124902 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -3.907124902 + -2.875 x = -3.907124902 + -2.875 Combine like terms: -3.907124902 + -2.875 = -6.782124902 x = -6.782124902 Simplifying x = -6.782124902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.032124902, -6.782124902}
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