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Simplifying -3x2 + x + 11 = 0 Reorder the terms: 11 + x + -3x2 = 0 Solving 11 + x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.666666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -0.3333333333x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -0.3333333333x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + 3.666666667 -0.3333333333x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -0.3333333333x + x2 = 3.666666667 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. -0.3333333333x + 0.25 + x2 = 3.666666667 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = 3.666666667 + 0.25 Combine like terms: 3.666666667 + 0.25 = 3.916666667 0.25 + -0.3333333333x + x2 = 3.916666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.916666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (x + 0.5) equal to 1.979057015 and -1.979057015.Subproblem 1
x + 0.5 = 1.979057015 Simplifying x + 0.5 = 1.979057015 Reorder the terms: 0.5 + x = 1.979057015 Solving 0.5 + x = 1.979057015 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 = 1.979057015 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.979057015 + -0.5 x = 1.979057015 + -0.5 Combine like terms: 1.979057015 + -0.5 = 1.479057015 x = 1.479057015 Simplifying x = 1.479057015Subproblem 2
x + 0.5 = -1.979057015 Simplifying x + 0.5 = -1.979057015 Reorder the terms: 0.5 + x = -1.979057015 Solving 0.5 + x = -1.979057015 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 = -1.979057015 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.979057015 + -0.5 x = -1.979057015 + -0.5 Combine like terms: -1.979057015 + -0.5 = -2.479057015 x = -2.479057015 Simplifying x = -2.479057015Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.479057015, -2.479057015}
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