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Simplifying 4x2 + 3x + -174 = 0 Reorder the terms: -174 + 3x + 4x2 = 0 Solving -174 + 3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -43.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + 0.75x + 43.5 + x2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + 0.75x + x2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + 0.75x + x2 = 0 + 43.5 0.75x + x2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 0.75x + x2 = 43.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 43.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 43.5 + 0.140625 Combine like terms: 43.5 + 0.140625 = 43.640625 0.140625 + 0.75x + x2 = 43.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 43.640625 Calculate the square root of the right side: 6.606105131 Break this problem into two subproblems by setting (x + 0.375) equal to 6.606105131 and -6.606105131.Subproblem 1
x + 0.375 = 6.606105131 Simplifying x + 0.375 = 6.606105131 Reorder the terms: 0.375 + x = 6.606105131 Solving 0.375 + x = 6.606105131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 6.606105131 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 6.606105131 + -0.375 x = 6.606105131 + -0.375 Combine like terms: 6.606105131 + -0.375 = 6.231105131 x = 6.231105131 Simplifying x = 6.231105131Subproblem 2
x + 0.375 = -6.606105131 Simplifying x + 0.375 = -6.606105131 Reorder the terms: 0.375 + x = -6.606105131 Solving 0.375 + x = -6.606105131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -6.606105131 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -6.606105131 + -0.375 x = -6.606105131 + -0.375 Combine like terms: -6.606105131 + -0.375 = -6.981105131 x = -6.981105131 Simplifying x = -6.981105131Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.231105131, -6.981105131}
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