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Simplifying 7(3.4225 + -3.7x + x2) = x2 (3.4225 * 7 + -3.7x * 7 + x2 * 7) = x2 (23.9575 + -25.9x + 7x2) = x2 Solving 23.9575 + -25.9x + 7x2 = x2 Solving for variable 'x'. Combine like terms: 7x2 + -1x2 = 6x2 23.9575 + -25.9x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23.9575 + -25.9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.992916667 + -4.316666667x + x2 = 0 Move the constant term to the right: Add '-3.992916667' to each side of the equation. 3.992916667 + -4.316666667x + -3.992916667 + x2 = 0 + -3.992916667 Reorder the terms: 3.992916667 + -3.992916667 + -4.316666667x + x2 = 0 + -3.992916667 Combine like terms: 3.992916667 + -3.992916667 = 0.000000000 0.000000000 + -4.316666667x + x2 = 0 + -3.992916667 -4.316666667x + x2 = 0 + -3.992916667 Combine like terms: 0 + -3.992916667 = -3.992916667 -4.316666667x + x2 = -3.992916667 The x term is -4.316666667x. Take half its coefficient (-2.158333334). Square it (4.658402781) and add it to both sides. Add '4.658402781' to each side of the equation. -4.316666667x + 4.658402781 + x2 = -3.992916667 + 4.658402781 Reorder the terms: 4.658402781 + -4.316666667x + x2 = -3.992916667 + 4.658402781 Combine like terms: -3.992916667 + 4.658402781 = 0.665486114 4.658402781 + -4.316666667x + x2 = 0.665486114 Factor a perfect square on the left side: (x + -2.158333334)(x + -2.158333334) = 0.665486114 Calculate the square root of the right side: 0.815773323 Break this problem into two subproblems by setting (x + -2.158333334) equal to 0.815773323 and -0.815773323.Subproblem 1
x + -2.158333334 = 0.815773323 Simplifying x + -2.158333334 = 0.815773323 Reorder the terms: -2.158333334 + x = 0.815773323 Solving -2.158333334 + x = 0.815773323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.158333334' to each side of the equation. -2.158333334 + 2.158333334 + x = 0.815773323 + 2.158333334 Combine like terms: -2.158333334 + 2.158333334 = 0.000000000 0.000000000 + x = 0.815773323 + 2.158333334 x = 0.815773323 + 2.158333334 Combine like terms: 0.815773323 + 2.158333334 = 2.974106657 x = 2.974106657 Simplifying x = 2.974106657Subproblem 2
x + -2.158333334 = -0.815773323 Simplifying x + -2.158333334 = -0.815773323 Reorder the terms: -2.158333334 + x = -0.815773323 Solving -2.158333334 + x = -0.815773323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.158333334' to each side of the equation. -2.158333334 + 2.158333334 + x = -0.815773323 + 2.158333334 Combine like terms: -2.158333334 + 2.158333334 = 0.000000000 0.000000000 + x = -0.815773323 + 2.158333334 x = -0.815773323 + 2.158333334 Combine like terms: -0.815773323 + 2.158333334 = 1.342560011 x = 1.342560011 Simplifying x = 1.342560011Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.974106657, 1.342560011}
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