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Simplifying 15x2 = -1(9x + 1) Reorder the terms: 15x2 = -1(1 + 9x) 15x2 = (1 * -1 + 9x * -1) 15x2 = (-1 + -9x) Solving 15x2 = -1 + -9x Solving for variable 'x'. Reorder the terms: 1 + 9x + 15x2 = -1 + -9x + 1 + 9x Reorder the terms: 1 + 9x + 15x2 = -1 + 1 + -9x + 9x Combine like terms: -1 + 1 = 0 1 + 9x + 15x2 = 0 + -9x + 9x 1 + 9x + 15x2 = -9x + 9x Combine like terms: -9x + 9x = 0 1 + 9x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.06666666667 + 0.6x + x2 = 0 Move the constant term to the right: Add '-0.06666666667' to each side of the equation. 0.06666666667 + 0.6x + -0.06666666667 + x2 = 0 + -0.06666666667 Reorder the terms: 0.06666666667 + -0.06666666667 + 0.6x + x2 = 0 + -0.06666666667 Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000 0.00000000000 + 0.6x + x2 = 0 + -0.06666666667 0.6x + x2 = 0 + -0.06666666667 Combine like terms: 0 + -0.06666666667 = -0.06666666667 0.6x + x2 = -0.06666666667 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 = -0.06666666667 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -0.06666666667 + 0.09 Combine like terms: -0.06666666667 + 0.09 = 0.02333333333 0.09 + 0.6x + x2 = 0.02333333333 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.02333333333 Calculate the square root of the right side: 0.152752523 Break this problem into two subproblems by setting (x + 0.3) equal to 0.152752523 and -0.152752523.Subproblem 1
x + 0.3 = 0.152752523 Simplifying x + 0.3 = 0.152752523 Reorder the terms: 0.3 + x = 0.152752523 Solving 0.3 + x = 0.152752523 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 = 0.152752523 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.152752523 + -0.3 x = 0.152752523 + -0.3 Combine like terms: 0.152752523 + -0.3 = -0.147247477 x = -0.147247477 Simplifying x = -0.147247477Subproblem 2
x + 0.3 = -0.152752523 Simplifying x + 0.3 = -0.152752523 Reorder the terms: 0.3 + x = -0.152752523 Solving 0.3 + x = -0.152752523 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 = -0.152752523 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.152752523 + -0.3 x = -0.152752523 + -0.3 Combine like terms: -0.152752523 + -0.3 = -0.452752523 x = -0.452752523 Simplifying x = -0.452752523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.147247477, -0.452752523}
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