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Simplifying 4x2 + -7x + -125 = 0 Reorder the terms: -125 + -7x + 4x2 = 0 Solving -125 + -7x + 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'. -31.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -1.75x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -1.75x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -1.75x + x2 = 0 + 31.25 -1.75x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -1.75x + x2 = 31.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 31.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 31.25 + 0.765625 Combine like terms: 31.25 + 0.765625 = 32.015625 0.765625 + -1.75x + x2 = 32.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 32.015625 Calculate the square root of the right side: 5.658235149 Break this problem into two subproblems by setting (x + -0.875) equal to 5.658235149 and -5.658235149.Subproblem 1
x + -0.875 = 5.658235149 Simplifying x + -0.875 = 5.658235149 Reorder the terms: -0.875 + x = 5.658235149 Solving -0.875 + x = 5.658235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 5.658235149 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 5.658235149 + 0.875 x = 5.658235149 + 0.875 Combine like terms: 5.658235149 + 0.875 = 6.533235149 x = 6.533235149 Simplifying x = 6.533235149Subproblem 2
x + -0.875 = -5.658235149 Simplifying x + -0.875 = -5.658235149 Reorder the terms: -0.875 + x = -5.658235149 Solving -0.875 + x = -5.658235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -5.658235149 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -5.658235149 + 0.875 x = -5.658235149 + 0.875 Combine like terms: -5.658235149 + 0.875 = -4.783235149 x = -4.783235149 Simplifying x = -4.783235149Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.533235149, -4.783235149}
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