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Simplifying 5x2 + -56x + 3 = 0 Reorder the terms: 3 + -56x + 5x2 = 0 Solving 3 + -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'. 0.6 + -11.2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -11.2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -11.2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -11.2x + x2 = 0 + -0.6 -11.2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -11.2x + x2 = -0.6 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 = -0.6 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = -0.6 + 31.36 Combine like terms: -0.6 + 31.36 = 30.76 31.36 + -11.2x + x2 = 30.76 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 30.76 Calculate the square root of the right side: 5.54616985 Break this problem into two subproblems by setting (x + -5.6) equal to 5.54616985 and -5.54616985.Subproblem 1
x + -5.6 = 5.54616985 Simplifying x + -5.6 = 5.54616985 Reorder the terms: -5.6 + x = 5.54616985 Solving -5.6 + x = 5.54616985 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 = 5.54616985 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 5.54616985 + 5.6 x = 5.54616985 + 5.6 Combine like terms: 5.54616985 + 5.6 = 11.14616985 x = 11.14616985 Simplifying x = 11.14616985Subproblem 2
x + -5.6 = -5.54616985 Simplifying x + -5.6 = -5.54616985 Reorder the terms: -5.6 + x = -5.54616985 Solving -5.6 + x = -5.54616985 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 = -5.54616985 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -5.54616985 + 5.6 x = -5.54616985 + 5.6 Combine like terms: -5.54616985 + 5.6 = 0.05383015 x = 0.05383015 Simplifying x = 0.05383015Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.14616985, 0.05383015}
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