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Simplifying 4x2 + 11x = 59 Reorder the terms: 11x + 4x2 = 59 Solving 11x + 4x2 = 59 Solving for variable 'x'. Reorder the terms: -59 + 11x + 4x2 = 59 + -59 Combine like terms: 59 + -59 = 0 -59 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14.75 + 2.75x + x2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + 2.75x + 14.75 + x2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + 2.75x + x2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + 2.75x + x2 = 0 + 14.75 2.75x + x2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 2.75x + x2 = 14.75 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 14.75 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 14.75 + 1.890625 Combine like terms: 14.75 + 1.890625 = 16.640625 1.890625 + 2.75x + x2 = 16.640625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 16.640625 Calculate the square root of the right side: 4.079292218 Break this problem into two subproblems by setting (x + 1.375) equal to 4.079292218 and -4.079292218.Subproblem 1
x + 1.375 = 4.079292218 Simplifying x + 1.375 = 4.079292218 Reorder the terms: 1.375 + x = 4.079292218 Solving 1.375 + x = 4.079292218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 4.079292218 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 4.079292218 + -1.375 x = 4.079292218 + -1.375 Combine like terms: 4.079292218 + -1.375 = 2.704292218 x = 2.704292218 Simplifying x = 2.704292218Subproblem 2
x + 1.375 = -4.079292218 Simplifying x + 1.375 = -4.079292218 Reorder the terms: 1.375 + x = -4.079292218 Solving 1.375 + x = -4.079292218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -4.079292218 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -4.079292218 + -1.375 x = -4.079292218 + -1.375 Combine like terms: -4.079292218 + -1.375 = -5.454292218 x = -5.454292218 Simplifying x = -5.454292218Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.704292218, -5.454292218}
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