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Simplifying 4x2 + 4x = 23 Reorder the terms: 4x + 4x2 = 23 Solving 4x + 4x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + 4x + 4x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x + x2 = 0 + 5.75 x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 x + x2 = 5.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.75 + 0.25 Combine like terms: 5.75 + 0.25 = 6 1.25 + x2 = 6 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 0.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 0.5 = 2.449489743 Simplifying x + 0.5 = 2.449489743 Reorder the terms: 0.5 + x = 2.449489743 Solving 0.5 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.449489743 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.449489743 + -0.5 x = 2.449489743 + -0.5 Combine like terms: 2.449489743 + -0.5 = 1.949489743 x = 1.949489743 Simplifying x = 1.949489743Subproblem 2
x + 0.5 = -2.449489743 Simplifying x + 0.5 = -2.449489743 Reorder the terms: 0.5 + x = -2.449489743 Solving 0.5 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.449489743 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.449489743 + -0.5 x = -2.449489743 + -0.5 Combine like terms: -2.449489743 + -0.5 = -2.949489743 x = -2.949489743 Simplifying x = -2.949489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.949489743, -2.949489743}
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