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Simplifying 4x2 + 3x + -150 = 0 Reorder the terms: -150 + 3x + 4x2 = 0 Solving -150 + 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'. -37.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 0.75x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 0.75x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 0.75x + x2 = 0 + 37.5 0.75x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 0.75x + x2 = 37.5 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 = 37.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 37.5 + 0.140625 Combine like terms: 37.5 + 0.140625 = 37.640625 0.140625 + 0.75x + x2 = 37.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 37.640625 Calculate the square root of the right side: 6.135195596 Break this problem into two subproblems by setting (x + 0.375) equal to 6.135195596 and -6.135195596.Subproblem 1
x + 0.375 = 6.135195596 Simplifying x + 0.375 = 6.135195596 Reorder the terms: 0.375 + x = 6.135195596 Solving 0.375 + x = 6.135195596 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 = 6.135195596 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 6.135195596 + -0.375 x = 6.135195596 + -0.375 Combine like terms: 6.135195596 + -0.375 = 5.760195596 x = 5.760195596 Simplifying x = 5.760195596Subproblem 2
x + 0.375 = -6.135195596 Simplifying x + 0.375 = -6.135195596 Reorder the terms: 0.375 + x = -6.135195596 Solving 0.375 + x = -6.135195596 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 = -6.135195596 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -6.135195596 + -0.375 x = -6.135195596 + -0.375 Combine like terms: -6.135195596 + -0.375 = -6.510195596 x = -6.510195596 Simplifying x = -6.510195596Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.760195596, -6.510195596}
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