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Simplifying 5x2 + -56x + -64 = 0 Reorder the terms: -64 + -56x + 5x2 = 0 Solving -64 + -56x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.8 + -11.2x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -11.2x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -11.2x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -11.2x + x2 = 0 + 12.8 -11.2x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -11.2x + x2 = 12.8 The x term is -11.2x. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2x + 31.36 + x2 = 12.8 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = 12.8 + 31.36 Combine like terms: 12.8 + 31.36 = 44.16 31.36 + -11.2x + x2 = 44.16 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 44.16 Calculate the square root of the right side: 6.64529909 Break this problem into two subproblems by setting (x + -5.6) equal to 6.64529909 and -6.64529909.Subproblem 1
x + -5.6 = 6.64529909 Simplifying x + -5.6 = 6.64529909 Reorder the terms: -5.6 + x = 6.64529909 Solving -5.6 + x = 6.64529909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = 6.64529909 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 6.64529909 + 5.6 x = 6.64529909 + 5.6 Combine like terms: 6.64529909 + 5.6 = 12.24529909 x = 12.24529909 Simplifying x = 12.24529909Subproblem 2
x + -5.6 = -6.64529909 Simplifying x + -5.6 = -6.64529909 Reorder the terms: -5.6 + x = -6.64529909 Solving -5.6 + x = -6.64529909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = -6.64529909 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -6.64529909 + 5.6 x = -6.64529909 + 5.6 Combine like terms: -6.64529909 + 5.6 = -1.04529909 x = -1.04529909 Simplifying x = -1.04529909Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.24529909, -1.04529909}
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