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Simplifying 4x2 + -56x + -45 = 0 Reorder the terms: -45 + -56x + 4x2 = 0 Solving -45 + -56x + 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'. -11.25 + -14x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -14x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -14x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -14x + x2 = 0 + 11.25 -14x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -14x + x2 = 11.25 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 11.25 + 49 Reorder the terms: 49 + -14x + x2 = 11.25 + 49 Combine like terms: 11.25 + 49 = 60.25 49 + -14x + x2 = 60.25 Factor a perfect square on the left side: (x + -7)(x + -7) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -7) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -7 = 7.762087348 Simplifying x + -7 = 7.762087348 Reorder the terms: -7 + x = 7.762087348 Solving -7 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.762087348 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.762087348 + 7 x = 7.762087348 + 7 Combine like terms: 7.762087348 + 7 = 14.762087348 x = 14.762087348 Simplifying x = 14.762087348Subproblem 2
x + -7 = -7.762087348 Simplifying x + -7 = -7.762087348 Reorder the terms: -7 + x = -7.762087348 Solving -7 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.762087348 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.762087348 + 7 x = -7.762087348 + 7 Combine like terms: -7.762087348 + 7 = -0.762087348 x = -0.762087348 Simplifying x = -0.762087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.762087348, -0.762087348}
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