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Simplifying 4x2 + 4x + -57 = 0 Reorder the terms: -57 + 4x + 4x2 = 0 Solving -57 + 4x + 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'. -14.25 + x + x2 = 0 Move the constant term to the right: Add '14.25' to each side of the equation. -14.25 + x + 14.25 + x2 = 0 + 14.25 Reorder the terms: -14.25 + 14.25 + x + x2 = 0 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + x + x2 = 0 + 14.25 x + x2 = 0 + 14.25 Combine like terms: 0 + 14.25 = 14.25 x + x2 = 14.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 14.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 14.25 + 0.25 Combine like terms: 14.25 + 0.25 = 14.5 1.25 + x2 = 14.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + 0.5) equal to 3.807886553 and -3.807886553.Subproblem 1
x + 0.5 = 3.807886553 Simplifying x + 0.5 = 3.807886553 Reorder the terms: 0.5 + x = 3.807886553 Solving 0.5 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.807886553 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.807886553 + -0.5 x = 3.807886553 + -0.5 Combine like terms: 3.807886553 + -0.5 = 3.307886553 x = 3.307886553 Simplifying x = 3.307886553Subproblem 2
x + 0.5 = -3.807886553 Simplifying x + 0.5 = -3.807886553 Reorder the terms: 0.5 + x = -3.807886553 Solving 0.5 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.807886553 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.807886553 + -0.5 x = -3.807886553 + -0.5 Combine like terms: -3.807886553 + -0.5 = -4.307886553 x = -4.307886553 Simplifying x = -4.307886553Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.307886553, -4.307886553}
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