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Simplifying 18 = 5x2 + 3x Reorder the terms: 18 = 3x + 5x2 Solving 18 = 3x + 5x2 Solving for variable 'x'. Reorder the terms: 18 + -3x + -5x2 = 3x + -3x + 5x2 + -5x2 Combine like terms: 3x + -3x = 0 18 + -3x + -5x2 = 0 + 5x2 + -5x2 18 + -3x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 18 + -3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.6 + 0.6x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 0.6x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 0.6x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 0.6x + x2 = 0 + 3.6 0.6x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 0.6x + x2 = 3.6 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 = 3.6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 3.6 + 0.09 Combine like terms: 3.6 + 0.09 = 3.69 0.09 + 0.6x + x2 = 3.69 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (x + 0.3) equal to 1.920937271 and -1.920937271.Subproblem 1
x + 0.3 = 1.920937271 Simplifying x + 0.3 = 1.920937271 Reorder the terms: 0.3 + x = 1.920937271 Solving 0.3 + x = 1.920937271 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 = 1.920937271 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.920937271 + -0.3 x = 1.920937271 + -0.3 Combine like terms: 1.920937271 + -0.3 = 1.620937271 x = 1.620937271 Simplifying x = 1.620937271Subproblem 2
x + 0.3 = -1.920937271 Simplifying x + 0.3 = -1.920937271 Reorder the terms: 0.3 + x = -1.920937271 Solving 0.3 + x = -1.920937271 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 = -1.920937271 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.920937271 + -0.3 x = -1.920937271 + -0.3 Combine like terms: -1.920937271 + -0.3 = -2.220937271 x = -2.220937271 Simplifying x = -2.220937271Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.620937271, -2.220937271}
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