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Simplifying 15 = 18x + -5x2 Solving 15 = 18x + -5x2 Solving for variable 'x'. Reorder the terms: 15 + -18x + 5x2 = 18x + -18x + -5x2 + 5x2 Combine like terms: 18x + -18x = 0 15 + -18x + 5x2 = 0 + -5x2 + 5x2 15 + -18x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 15 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -3.6x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3.6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -3.6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3.6x + x2 = 0 + -3 -3.6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3.6x + x2 = -3 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -3 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -3 + 3.24 Combine like terms: -3 + 3.24 = 0.24 3.24 + -3.6x + x2 = 0.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + -1.8) equal to 0.489897949 and -0.489897949.Subproblem 1
x + -1.8 = 0.489897949 Simplifying x + -1.8 = 0.489897949 Reorder the terms: -1.8 + x = 0.489897949 Solving -1.8 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.489897949 + 1.8 x = 0.489897949 + 1.8 Combine like terms: 0.489897949 + 1.8 = 2.289897949 x = 2.289897949 Simplifying x = 2.289897949Subproblem 2
x + -1.8 = -0.489897949 Simplifying x + -1.8 = -0.489897949 Reorder the terms: -1.8 + x = -0.489897949 Solving -1.8 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.489897949 + 1.8 x = -0.489897949 + 1.8 Combine like terms: -0.489897949 + 1.8 = 1.310102051 x = 1.310102051 Simplifying x = 1.310102051Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.289897949, 1.310102051}
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