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Simplifying 7.6x + 2.75x2 = -1.76 Solving 7.6x + 2.75x2 = -1.76 Solving for variable 'x'. Reorder the terms: 1.76 + 7.6x + 2.75x2 = -1.76 + 1.76 Combine like terms: -1.76 + 1.76 = 0.00 1.76 + 7.6x + 2.75x2 = 0.00 Begin completing the square. Divide all terms by 2.75 the coefficient of the squared term: Divide each side by '2.75'. 0.64 + 2.763636364x + x2 = 0 Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + 2.763636364x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + 2.763636364x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + 2.763636364x + x2 = 0 + -0.64 2.763636364x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 2.763636364x + x2 = -0.64 The x term is 2.763636364x. Take half its coefficient (1.381818182). Square it (1.909421488) and add it to both sides. Add '1.909421488' to each side of the equation. 2.763636364x + 1.909421488 + x2 = -0.64 + 1.909421488 Reorder the terms: 1.909421488 + 2.763636364x + x2 = -0.64 + 1.909421488 Combine like terms: -0.64 + 1.909421488 = 1.269421488 1.909421488 + 2.763636364x + x2 = 1.269421488 Factor a perfect square on the left side: (x + 1.381818182)(x + 1.381818182) = 1.269421488 Calculate the square root of the right side: 1.126686065 Break this problem into two subproblems by setting (x + 1.381818182) equal to 1.126686065 and -1.126686065.Subproblem 1
x + 1.381818182 = 1.126686065 Simplifying x + 1.381818182 = 1.126686065 Reorder the terms: 1.381818182 + x = 1.126686065 Solving 1.381818182 + x = 1.126686065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.381818182' to each side of the equation. 1.381818182 + -1.381818182 + x = 1.126686065 + -1.381818182 Combine like terms: 1.381818182 + -1.381818182 = 0.000000000 0.000000000 + x = 1.126686065 + -1.381818182 x = 1.126686065 + -1.381818182 Combine like terms: 1.126686065 + -1.381818182 = -0.255132117 x = -0.255132117 Simplifying x = -0.255132117Subproblem 2
x + 1.381818182 = -1.126686065 Simplifying x + 1.381818182 = -1.126686065 Reorder the terms: 1.381818182 + x = -1.126686065 Solving 1.381818182 + x = -1.126686065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.381818182' to each side of the equation. 1.381818182 + -1.381818182 + x = -1.126686065 + -1.381818182 Combine like terms: 1.381818182 + -1.381818182 = 0.000000000 0.000000000 + x = -1.126686065 + -1.381818182 x = -1.126686065 + -1.381818182 Combine like terms: -1.126686065 + -1.381818182 = -2.508504247 x = -2.508504247 Simplifying x = -2.508504247Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.255132117, -2.508504247}
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