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Simplifying 4x2 + 4x + -100.5 = 0 Reorder the terms: -100.5 + 4x + 4x2 = 0 Solving -100.5 + 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'. -25.125 + x + x2 = 0 Move the constant term to the right: Add '25.125' to each side of the equation. -25.125 + x + 25.125 + x2 = 0 + 25.125 Reorder the terms: -25.125 + 25.125 + x + x2 = 0 + 25.125 Combine like terms: -25.125 + 25.125 = 0.000 0.000 + x + x2 = 0 + 25.125 x + x2 = 0 + 25.125 Combine like terms: 0 + 25.125 = 25.125 x + x2 = 25.125 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 = 25.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 25.125 + 0.25 Combine like terms: 25.125 + 0.25 = 25.375 1.25 + x2 = 25.375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 25.375 Calculate the square root of the right side: 5.03736042 Break this problem into two subproblems by setting (x + 0.5) equal to 5.03736042 and -5.03736042.Subproblem 1
x + 0.5 = 5.03736042 Simplifying x + 0.5 = 5.03736042 Reorder the terms: 0.5 + x = 5.03736042 Solving 0.5 + x = 5.03736042 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 = 5.03736042 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.03736042 + -0.5 x = 5.03736042 + -0.5 Combine like terms: 5.03736042 + -0.5 = 4.53736042 x = 4.53736042 Simplifying x = 4.53736042Subproblem 2
x + 0.5 = -5.03736042 Simplifying x + 0.5 = -5.03736042 Reorder the terms: 0.5 + x = -5.03736042 Solving 0.5 + x = -5.03736042 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 = -5.03736042 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.03736042 + -0.5 x = -5.03736042 + -0.5 Combine like terms: -5.03736042 + -0.5 = -5.53736042 x = -5.53736042 Simplifying x = -5.53736042Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.53736042, -5.53736042}
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