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Simplifying 15 = 5 + 27x + -15x2 Solving 15 = 5 + 27x + -15x2 Solving for variable 'x'. Combine like terms: 15 + -5 = 10 10 + -27x + 15x2 = 5 + 27x + -15x2 + -5 + -27x + 15x2 Reorder the terms: 10 + -27x + 15x2 = 5 + -5 + 27x + -27x + -15x2 + 15x2 Combine like terms: 5 + -5 = 0 10 + -27x + 15x2 = 0 + 27x + -27x + -15x2 + 15x2 10 + -27x + 15x2 = 27x + -27x + -15x2 + 15x2 Combine like terms: 27x + -27x = 0 10 + -27x + 15x2 = 0 + -15x2 + 15x2 10 + -27x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 10 + -27x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.6666666667 + -1.8x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.8x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.8x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.8x + x2 = 0 + -0.6666666667 -1.8x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.8x + x2 = -0.6666666667 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = -0.6666666667 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.6666666667 + 0.81 Combine like terms: -0.6666666667 + 0.81 = 0.1433333333 0.81 + -1.8x + x2 = 0.1433333333 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.1433333333 Calculate the square root of the right side: 0.37859389 Break this problem into two subproblems by setting (x + -0.9) equal to 0.37859389 and -0.37859389.Subproblem 1
x + -0.9 = 0.37859389 Simplifying x + -0.9 = 0.37859389 Reorder the terms: -0.9 + x = 0.37859389 Solving -0.9 + x = 0.37859389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.37859389 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.37859389 + 0.9 x = 0.37859389 + 0.9 Combine like terms: 0.37859389 + 0.9 = 1.27859389 x = 1.27859389 Simplifying x = 1.27859389Subproblem 2
x + -0.9 = -0.37859389 Simplifying x + -0.9 = -0.37859389 Reorder the terms: -0.9 + x = -0.37859389 Solving -0.9 + x = -0.37859389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -0.37859389 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.37859389 + 0.9 x = -0.37859389 + 0.9 Combine like terms: -0.37859389 + 0.9 = 0.52140611 x = 0.52140611 Simplifying x = 0.52140611Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27859389, 0.52140611}
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