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Simplifying 79x(104x + -74) = 11 Reorder the terms: 79x(-74 + 104x) = 11 (-74 * 79x + 104x * 79x) = 11 (-5846x + 8216x2) = 11 Solving -5846x + 8216x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -5846x + 8216x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -5846x + 8216x2 = 0 Begin completing the square. Divide all terms by 8216 the coefficient of the squared term: Divide each side by '8216'. -0.001338851022 + -0.7115384615x + x2 = 0 Move the constant term to the right: Add '0.001338851022' to each side of the equation. -0.001338851022 + -0.7115384615x + 0.001338851022 + x2 = 0 + 0.001338851022 Reorder the terms: -0.001338851022 + 0.001338851022 + -0.7115384615x + x2 = 0 + 0.001338851022 Combine like terms: -0.001338851022 + 0.001338851022 = 0.000000000000 0.000000000000 + -0.7115384615x + x2 = 0 + 0.001338851022 -0.7115384615x + x2 = 0 + 0.001338851022 Combine like terms: 0 + 0.001338851022 = 0.001338851022 -0.7115384615x + x2 = 0.001338851022 The x term is -0.7115384615x. Take half its coefficient (-0.3557692308). Square it (0.1265717456) and add it to both sides. Add '0.1265717456' to each side of the equation. -0.7115384615x + 0.1265717456 + x2 = 0.001338851022 + 0.1265717456 Reorder the terms: 0.1265717456 + -0.7115384615x + x2 = 0.001338851022 + 0.1265717456 Combine like terms: 0.001338851022 + 0.1265717456 = 0.127910596622 0.1265717456 + -0.7115384615x + x2 = 0.127910596622 Factor a perfect square on the left side: (x + -0.3557692308)(x + -0.3557692308) = 0.127910596622 Calculate the square root of the right side: 0.35764591 Break this problem into two subproblems by setting (x + -0.3557692308) equal to 0.35764591 and -0.35764591.Subproblem 1
x + -0.3557692308 = 0.35764591 Simplifying x + -0.3557692308 = 0.35764591 Reorder the terms: -0.3557692308 + x = 0.35764591 Solving -0.3557692308 + x = 0.35764591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3557692308' to each side of the equation. -0.3557692308 + 0.3557692308 + x = 0.35764591 + 0.3557692308 Combine like terms: -0.3557692308 + 0.3557692308 = 0.0000000000 0.0000000000 + x = 0.35764591 + 0.3557692308 x = 0.35764591 + 0.3557692308 Combine like terms: 0.35764591 + 0.3557692308 = 0.7134151408 x = 0.7134151408 Simplifying x = 0.7134151408Subproblem 2
x + -0.3557692308 = -0.35764591 Simplifying x + -0.3557692308 = -0.35764591 Reorder the terms: -0.3557692308 + x = -0.35764591 Solving -0.3557692308 + x = -0.35764591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3557692308' to each side of the equation. -0.3557692308 + 0.3557692308 + x = -0.35764591 + 0.3557692308 Combine like terms: -0.3557692308 + 0.3557692308 = 0.0000000000 0.0000000000 + x = -0.35764591 + 0.3557692308 x = -0.35764591 + 0.3557692308 Combine like terms: -0.35764591 + 0.3557692308 = -0.0018766792 x = -0.0018766792 Simplifying x = -0.0018766792Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7134151408, -0.0018766792}
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