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Simplifying 5x2 + -22x + 23 = 0 Reorder the terms: 23 + -22x + 5x2 = 0 Solving 23 + -22x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.6 + -4.4x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + -4.4x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + -4.4x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + -4.4x + x2 = 0 + -4.6 -4.4x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 -4.4x + x2 = -4.6 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -4.6 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -4.6 + 4.84 Combine like terms: -4.6 + 4.84 = 0.24 4.84 + -4.4x + x2 = 0.24 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + -2.2) equal to 0.489897949 and -0.489897949.Subproblem 1
x + -2.2 = 0.489897949 Simplifying x + -2.2 = 0.489897949 Reorder the terms: -2.2 + x = 0.489897949 Solving -2.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 0.489897949 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 0.489897949 + 2.2 x = 0.489897949 + 2.2 Combine like terms: 0.489897949 + 2.2 = 2.689897949 x = 2.689897949 Simplifying x = 2.689897949Subproblem 2
x + -2.2 = -0.489897949 Simplifying x + -2.2 = -0.489897949 Reorder the terms: -2.2 + x = -0.489897949 Solving -2.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -0.489897949 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -0.489897949 + 2.2 x = -0.489897949 + 2.2 Combine like terms: -0.489897949 + 2.2 = 1.710102051 x = 1.710102051 Simplifying x = 1.710102051Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.689897949, 1.710102051}
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