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Simplifying 4x2 + 5x = 11 Reorder the terms: 5x + 4x2 = 11 Solving 5x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 5x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 1.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 1.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 1.25x + x2 = 0 + 2.75 1.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 1.25x + x2 = 2.75 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2.75 + 0.390625 Combine like terms: 2.75 + 0.390625 = 3.140625 0.390625 + 1.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 0.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 0.625 = 1.77218086 Simplifying x + 0.625 = 1.77218086 Reorder the terms: 0.625 + x = 1.77218086 Solving 0.625 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.77218086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.77218086 + -0.625 x = 1.77218086 + -0.625 Combine like terms: 1.77218086 + -0.625 = 1.14718086 x = 1.14718086 Simplifying x = 1.14718086Subproblem 2
x + 0.625 = -1.77218086 Simplifying x + 0.625 = -1.77218086 Reorder the terms: 0.625 + x = -1.77218086 Solving 0.625 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.77218086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.77218086 + -0.625 x = -1.77218086 + -0.625 Combine like terms: -1.77218086 + -0.625 = -2.39718086 x = -2.39718086 Simplifying x = -2.39718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.14718086, -2.39718086}
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