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Simplifying 4x2 + 10x = 11 Reorder the terms: 10x + 4x2 = 11 Solving 10x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 10x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 2.5x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 2.5x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 2.5x + x2 = 0 + 2.75 2.5x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 2.5x + x2 = 2.75 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 2.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 2.75 + 1.5625 Combine like terms: 2.75 + 1.5625 = 4.3125 1.5625 + 2.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + 1.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + 1.25 = 2.076655966 Simplifying x + 1.25 = 2.076655966 Reorder the terms: 1.25 + x = 2.076655966 Solving 1.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.076655966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.076655966 + -1.25 x = 2.076655966 + -1.25 Combine like terms: 2.076655966 + -1.25 = 0.826655966 x = 0.826655966 Simplifying x = 0.826655966Subproblem 2
x + 1.25 = -2.076655966 Simplifying x + 1.25 = -2.076655966 Reorder the terms: 1.25 + x = -2.076655966 Solving 1.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.076655966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.076655966 + -1.25 x = -2.076655966 + -1.25 Combine like terms: -2.076655966 + -1.25 = -3.326655966 x = -3.326655966 Simplifying x = -3.326655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.826655966, -3.326655966}
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