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Simplifying 0 = -5x2 + 3x + 11 Reorder the terms: 0 = 11 + 3x + -5x2 Solving 0 = 11 + 3x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -3x + 5x2 = 11 + 3x + -5x2 + -11 + -3x + 5x2 Reorder the terms: -11 + -3x + 5x2 = 11 + -11 + 3x + -3x + -5x2 + 5x2 Combine like terms: 11 + -11 = 0 -11 + -3x + 5x2 = 0 + 3x + -3x + -5x2 + 5x2 -11 + -3x + 5x2 = 3x + -3x + -5x2 + 5x2 Combine like terms: 3x + -3x = 0 -11 + -3x + 5x2 = 0 + -5x2 + 5x2 -11 + -3x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -11 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -0.6x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -0.6x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -0.6x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -0.6x + x2 = 0 + 2.2 -0.6x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -0.6x + x2 = 2.2 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 2.2 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 2.2 + 0.09 Combine like terms: 2.2 + 0.09 = 2.29 0.09 + -0.6x + x2 = 2.29 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (x + -0.3) equal to 1.513274595 and -1.513274595.Subproblem 1
x + -0.3 = 1.513274595 Simplifying x + -0.3 = 1.513274595 Reorder the terms: -0.3 + x = 1.513274595 Solving -0.3 + x = 1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.513274595 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.513274595 + 0.3 x = 1.513274595 + 0.3 Combine like terms: 1.513274595 + 0.3 = 1.813274595 x = 1.813274595 Simplifying x = 1.813274595Subproblem 2
x + -0.3 = -1.513274595 Simplifying x + -0.3 = -1.513274595 Reorder the terms: -0.3 + x = -1.513274595 Solving -0.3 + x = -1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.513274595 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.513274595 + 0.3 x = -1.513274595 + 0.3 Combine like terms: -1.513274595 + 0.3 = -1.213274595 x = -1.213274595 Simplifying x = -1.213274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.813274595, -1.213274595}
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