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Simplifying -4.9x2 + 34.3x + -58.8 = 0 Reorder the terms: -58.8 + 34.3x + -4.9x2 = 0 Solving -58.8 + 34.3x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 12 + -7x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7x + x2 = 0 + -12 -7x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7x + x2 = -12 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 = -12 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -12 + 12.25 Combine like terms: -12 + 12.25 = 0.25 12.25 + -7x + x2 = 0.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -3.5) equal to 0.5 and -0.5.Subproblem 1
x + -3.5 = 0.5 Simplifying x + -3.5 = 0.5 Reorder the terms: -3.5 + x = 0.5 Solving -3.5 + x = 0.5 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 = 0.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 0.5 + 3.5 x = 0.5 + 3.5 Combine like terms: 0.5 + 3.5 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -3.5 = -0.5 Simplifying x + -3.5 = -0.5 Reorder the terms: -3.5 + x = -0.5 Solving -3.5 + x = -0.5 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 = -0.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -0.5 + 3.5 x = -0.5 + 3.5 Combine like terms: -0.5 + 3.5 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 3}
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