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Simplifying 7.69x2 + 2.73x = 5.36 Reorder the terms: 2.73x + 7.69x2 = 5.36 Solving 2.73x + 7.69x2 = 5.36 Solving for variable 'x'. Reorder the terms: -5.36 + 2.73x + 7.69x2 = 5.36 + -5.36 Combine like terms: 5.36 + -5.36 = 0.00 -5.36 + 2.73x + 7.69x2 = 0.00 Begin completing the square. Divide all terms by 7.69 the coefficient of the squared term: Divide each side by '7.69'. -0.6970091027 + 0.355006502x + x2 = 0 Move the constant term to the right: Add '0.6970091027' to each side of the equation. -0.6970091027 + 0.355006502x + 0.6970091027 + x2 = 0 + 0.6970091027 Reorder the terms: -0.6970091027 + 0.6970091027 + 0.355006502x + x2 = 0 + 0.6970091027 Combine like terms: -0.6970091027 + 0.6970091027 = 0.0000000000 0.0000000000 + 0.355006502x + x2 = 0 + 0.6970091027 0.355006502x + x2 = 0 + 0.6970091027 Combine like terms: 0 + 0.6970091027 = 0.6970091027 0.355006502x + x2 = 0.6970091027 The x term is 0.355006502x. Take half its coefficient (0.177503251). Square it (0.03150740412) and add it to both sides. Add '0.03150740412' to each side of the equation. 0.355006502x + 0.03150740412 + x2 = 0.6970091027 + 0.03150740412 Reorder the terms: 0.03150740412 + 0.355006502x + x2 = 0.6970091027 + 0.03150740412 Combine like terms: 0.6970091027 + 0.03150740412 = 0.72851650682 0.03150740412 + 0.355006502x + x2 = 0.72851650682 Factor a perfect square on the left side: (x + 0.177503251)(x + 0.177503251) = 0.72851650682 Calculate the square root of the right side: 0.853531784 Break this problem into two subproblems by setting (x + 0.177503251) equal to 0.853531784 and -0.853531784.Subproblem 1
x + 0.177503251 = 0.853531784 Simplifying x + 0.177503251 = 0.853531784 Reorder the terms: 0.177503251 + x = 0.853531784 Solving 0.177503251 + x = 0.853531784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.177503251' to each side of the equation. 0.177503251 + -0.177503251 + x = 0.853531784 + -0.177503251 Combine like terms: 0.177503251 + -0.177503251 = 0.000000000 0.000000000 + x = 0.853531784 + -0.177503251 x = 0.853531784 + -0.177503251 Combine like terms: 0.853531784 + -0.177503251 = 0.676028533 x = 0.676028533 Simplifying x = 0.676028533Subproblem 2
x + 0.177503251 = -0.853531784 Simplifying x + 0.177503251 = -0.853531784 Reorder the terms: 0.177503251 + x = -0.853531784 Solving 0.177503251 + x = -0.853531784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.177503251' to each side of the equation. 0.177503251 + -0.177503251 + x = -0.853531784 + -0.177503251 Combine like terms: 0.177503251 + -0.177503251 = 0.000000000 0.000000000 + x = -0.853531784 + -0.177503251 x = -0.853531784 + -0.177503251 Combine like terms: -0.853531784 + -0.177503251 = -1.031035035 x = -1.031035035 Simplifying x = -1.031035035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.676028533, -1.031035035}
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