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Simplifying -4.9x2 + 34.3x + 1.5 = 6 Reorder the terms: 1.5 + 34.3x + -4.9x2 = 6 Solving 1.5 + 34.3x + -4.9x2 = 6 Solving for variable 'x'. Reorder the terms: 1.5 + -6 + 34.3x + -4.9x2 = 6 + -6 Combine like terms: 1.5 + -6 = -4.5 -4.5 + 34.3x + -4.9x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -4.5 + 34.3x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.9183673469 + -7x + x2 = 0 Move the constant term to the right: Add '-0.9183673469' to each side of the equation. 0.9183673469 + -7x + -0.9183673469 + x2 = 0 + -0.9183673469 Reorder the terms: 0.9183673469 + -0.9183673469 + -7x + x2 = 0 + -0.9183673469 Combine like terms: 0.9183673469 + -0.9183673469 = 0.0000000000 0.0000000000 + -7x + x2 = 0 + -0.9183673469 -7x + x2 = 0 + -0.9183673469 Combine like terms: 0 + -0.9183673469 = -0.9183673469 -7x + x2 = -0.9183673469 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.9183673469 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.9183673469 + 12.25 Combine like terms: -0.9183673469 + 12.25 = 11.3316326531 12.25 + -7x + x2 = 11.3316326531 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.3316326531 Calculate the square root of the right side: 3.366249048 Break this problem into two subproblems by setting (x + -3.5) equal to 3.366249048 and -3.366249048.Subproblem 1
x + -3.5 = 3.366249048 Simplifying x + -3.5 = 3.366249048 Reorder the terms: -3.5 + x = 3.366249048 Solving -3.5 + x = 3.366249048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.366249048 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.366249048 + 3.5 x = 3.366249048 + 3.5 Combine like terms: 3.366249048 + 3.5 = 6.866249048 x = 6.866249048 Simplifying x = 6.866249048Subproblem 2
x + -3.5 = -3.366249048 Simplifying x + -3.5 = -3.366249048 Reorder the terms: -3.5 + x = -3.366249048 Solving -3.5 + x = -3.366249048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.366249048 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.366249048 + 3.5 x = -3.366249048 + 3.5 Combine like terms: -3.366249048 + 3.5 = 0.133750952 x = 0.133750952 Simplifying x = 0.133750952Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.866249048, 0.133750952}
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