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Simplifying x2 + -0.75x = 19 Reorder the terms: -0.75x + x2 = 19 Solving -0.75x + x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -0.75x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -0.75x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -0.75x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -0.75x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -0.75x + x2 = 0 + 19 -0.75x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -0.75x + x2 = 19 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 = 19 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 19 + 0.140625 Combine like terms: 19 + 0.140625 = 19.140625 0.140625 + -0.75x + x2 = 19.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 19.140625 Calculate the square root of the right side: 4.375 Break this problem into two subproblems by setting (x + -0.375) equal to 4.375 and -4.375.Subproblem 1
x + -0.375 = 4.375 Simplifying x + -0.375 = 4.375 Reorder the terms: -0.375 + x = 4.375 Solving -0.375 + x = 4.375 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 = 4.375 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.375 + 0.375 x = 4.375 + 0.375 Combine like terms: 4.375 + 0.375 = 4.75 x = 4.75 Simplifying x = 4.75Subproblem 2
x + -0.375 = -4.375 Simplifying x + -0.375 = -4.375 Reorder the terms: -0.375 + x = -4.375 Solving -0.375 + x = -4.375 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 = -4.375 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.375 + 0.375 x = -4.375 + 0.375 Combine like terms: -4.375 + 0.375 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.75, -4}
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