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Simplifying -0.4x2 + 4.95x + -4 = 0 Reorder the terms: -4 + 4.95x + -0.4x2 = 0 Solving -4 + 4.95x + -0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 10 + -12.375x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -12.375x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -12.375x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -12.375x + x2 = 0 + -10 -12.375x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -12.375x + x2 = -10 The x term is -12.375x. Take half its coefficient (-6.1875). Square it (38.28515625) and add it to both sides. Add '38.28515625' to each side of the equation. -12.375x + 38.28515625 + x2 = -10 + 38.28515625 Reorder the terms: 38.28515625 + -12.375x + x2 = -10 + 38.28515625 Combine like terms: -10 + 38.28515625 = 28.28515625 38.28515625 + -12.375x + x2 = 28.28515625 Factor a perfect square on the left side: (x + -6.1875)(x + -6.1875) = 28.28515625 Calculate the square root of the right side: 5.3183791 Break this problem into two subproblems by setting (x + -6.1875) equal to 5.3183791 and -5.3183791.Subproblem 1
x + -6.1875 = 5.3183791 Simplifying x + -6.1875 = 5.3183791 Reorder the terms: -6.1875 + x = 5.3183791 Solving -6.1875 + x = 5.3183791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.1875' to each side of the equation. -6.1875 + 6.1875 + x = 5.3183791 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + x = 5.3183791 + 6.1875 x = 5.3183791 + 6.1875 Combine like terms: 5.3183791 + 6.1875 = 11.5058791 x = 11.5058791 Simplifying x = 11.5058791Subproblem 2
x + -6.1875 = -5.3183791 Simplifying x + -6.1875 = -5.3183791 Reorder the terms: -6.1875 + x = -5.3183791 Solving -6.1875 + x = -5.3183791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.1875' to each side of the equation. -6.1875 + 6.1875 + x = -5.3183791 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + x = -5.3183791 + 6.1875 x = -5.3183791 + 6.1875 Combine like terms: -5.3183791 + 6.1875 = 0.8691209 x = 0.8691209 Simplifying x = 0.8691209Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.5058791, 0.8691209}
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